4. Q4a
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Similar Question 1
<p>Rewrite each expression as an equivalent expression with a positive exponent.</p><p><code class='latex inline'>\displaystyle -(-5)^{-2} </code></p>
Similar Question 2
<p>Evaluate the expression for the given values. Express answers in rational form.</p><p><code class='latex inline'>\displaystyle \frac{8m^{-5}}{(2m)^{-3}} </code> where <code class='latex inline'>x = 4</code></p>
Similar Question 3
<p>Explain the difference between evaluating <code class='latex inline'>(-10)^{4}</code> and evaluating <code class='latex inline'>-10^{4}</code>.</p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>Write as a single power. Express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{(-4)^{6}(-4)^{3}}{\left((-4)^{9}\right)^{2}} </code></p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle 2^8 \times \left(\frac{2^{-5}}{2^6}\right) </code></p>
<p>Apply the quotient rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>(\dfrac{3}{4})^6 \div (\dfrac{3}{4})^3</code></p>
<p>Write as a single power. Express answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{6^{10}}{\left(6^{6}\right)^{2}} </code></p>
<p>Write as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>\displaystyle 3^{2} \times 3^{3} \times 3 </code></p>
<p>Evaluate.</p><p><code class='latex inline'>(\frac{3}{4})^{-3}</code></p>
<p>Simplify using the exponent laws. Then, evaluate.</p><p><code class='latex inline'>(2^3)^2\times (2^2)^3</code></p>
<p>Evaluate the expression. Then write the expressions in order from greatest to least.</p><p><code class='latex inline'>\displaystyle 7^2, 2^7, 4^5, 5^4 </code></p>
<p>Evaluate</p><p><code class='latex inline'> \displaystyle 13^0 </code></p>
<p>Apply the quotient rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>(-1)^{35} \div (-1)^{20}</code></p>
<p>Recall that <code class='latex inline'>a^2 =a \times a</code> and <code class='latex inline'>a^3 = a \times a \times a</code>. </p><p>Calculate each power for <code class='latex inline'>a = \frac{2}{3}</code>.</p> <ul> <li>i. <code class='latex inline'>a^2</code></li> <li>ii. <code class='latex inline'>a^3</code></li> <li>iii. <code class='latex inline'>a^4</code></li> </ul> <p>Why does a higher power of <code class='latex inline'>\displaystyle \frac{2}{3} </code> result in a lower product?</p>
<p>Simplify, then evaluate each expression. Leave answers as fractions or integers.</p><p><code class='latex inline'>\displaystyle \left(\frac{5^{-2}}{5}\right)^{-1} </code></p>
<p>Write as a single power. Express answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{11^{5}}{11^{9}} </code></p>
<p>Rewrite each expression as an equivalent expression with a positive exponent.</p><p><code class='latex inline'>\displaystyle \left(\frac{7}{3}\right)^{-5} </code></p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle (-8)^3(-8)^{-3} </code></p>
<p>Simplify, then evaluate each expression. Leave answers as fractions or integers.</p><p><code class='latex inline'>\displaystyle 13^{3} \times 13^{-4} </code></p>
<p>Simplify using the exponent laws. Then, evaluate.</p><p><code class='latex inline'>(2^6)^3\div (2^4)^4</code></p>
<p>Simplify using the exponent laws. Then, evaluate.</p><p><code class='latex inline'>\dfrac{0.2^4\times 0.2^3}{(0.2^2)^2}</code></p>
<p>Evaluate each expression.</p><p><code class='latex inline'>\displaystyle 9^{2} </code></p>
<p>Evaluate each expression. <code class='latex inline'>\displaystyle 9^{2} </code></p>
<p>Evaluate. </p><p><code class='latex inline'> (\dfrac{3}{4})^{-2}</code></p>
<p>Evaluate.</p><p><code class='latex inline'>(-1)^{99}</code></p>
<p>Evaluate.</p><p><code class='latex inline'>\displaystyle (-2)^{6} </code></p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle (7^{-1})^2 </code></p>
<p>Evaluate. </p><p><code class='latex inline'> (-\dfrac{1}{2})^{-3}</code></p>
<p>Evaluate.</p><p>a) <code class='latex inline'>\displaystyle 7^{-2} </code></p><p>b) <code class='latex inline'>\displaystyle -3^0 </code></p>
<p>Evaluate. </p><p><code class='latex inline'> -5 ^ {-2}</code></p>
<p>Simplify. then evaluate without using a calculator.</p><p><code class='latex inline'> \displaystyle (\frac{5}{4})^5(\frac{5}{4})^3\div (\frac{5}{4})^6 </code></p>
<p>Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'> \displaystyle [(7^{-3})^{-2}]^{-2} </code></p>
<p>Write each power in simplified form.</p><p><code class='latex inline'>9^5</code> as a base 3 power</p>
<p>Evaluate for <code class='latex inline'>x=2, y=1, </code> and <code class='latex inline'>z=3</code>. </p><p><code class='latex inline'>\displaystyle 3 y^{2}+4 z^{2}-2 x^{2} </code></p>
<p>Evaluate each expression.</p><p><code class='latex inline'>\displaystyle (-6)^{2} </code></p>
<p>Simplify. then evaluate without using a calculator.</p><p><code class='latex inline'> \displaystyle ((\frac{2}{5})^2)^2 </code></p>
<p>Rewrite the power with a positive exponent. </p><p><code class='latex inline'> 7 ^ {-2}</code></p>
<p>Rewrite the power with a positive exponent. </p><p><code class='latex inline'> (-4)^ {-2}</code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle \left(\frac{1}{5}\right)^{-1} + \left(-\frac{1}{2}\right)^{-2} </code></p>
<p>Evaluate</p><p><code class='latex inline'> \displaystyle (-6)^{-1} </code></p>
<p>Rewrite each expression as an equivalent expression with a positive exponent.</p><p><code class='latex inline'>\displaystyle \frac{1}{8^{-2}} </code></p>
<p>Evaluate. </p><p><code class='latex inline'> 2^{-5}</code></p>
<p>Evaluate each expression.</p><p><code class='latex inline'>\displaystyle (-1.8)^{2} </code></p>
<p>Which is greater: <code class='latex inline'>(\frac{1}{4})^2</code> or <code class='latex inline'>3^{-2}</code>. Show your reason without using a calculator.</p>
<p>Evaluate the expression for the given values. Express answers in rational form.</p><p><code class='latex inline'>\displaystyle (5x)^2(2x)^3 </code> where <code class='latex inline'>x = -2</code></p>
<p>Evaluate.</p><p><code class='latex inline'> \displaystyle 2^{-3} </code></p>
<p>Simplify. Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'>\displaystyle \frac{9^{4}\left(9^{3}\right)}{9^{12}} </code></p>
<p>Evaluate each expression without using a calculator.</p><p><code class='latex inline'>\displaystyle (8)^{0} </code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle (-6)^{-3} </code></p>
<p>Evaluate the power. Express your answer in rational form.</p><p> <code class='latex inline'>\displaystyle -7^{0}</code> </p>
<p>what is the simplified form of each expression?</p><p><code class='latex inline'>\displaystyle 2^{3} </code></p>
<p>Write <code class='latex inline'>2^8</code> as a power with a base that is different than the on you chose in part (a).</p>
<p>Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'> \displaystyle (-10)^8(-10)^{-8} </code></p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle 10^{8} </code></p>
<p>Evaluate.</p><p><code class='latex inline'>(-1)^{12}</code></p>
<p>Evaluate the power. Express your answer in rational form.</p><p><code class='latex inline'>\displaystyle 3^{-4} </code></p>
<p>Evaluate.</p><p><code class='latex inline'> \displaystyle 4^{-3} </code></p>
<p>Simplify. Write as a single power.</p><p><code class='latex inline'> \displaystyle \frac{(4^7)^3}{4^9(4^{11})} </code></p>
<p>Francesca is helping her friends Sasha and Vanessa study for a quiz. They are working on simplifying <code class='latex inline'> 2^{-2} \times 2 </code> . Francesca notices errors in each of her friends&#39; solutions, shown here:</p><p><code class='latex inline'> \begin{array}{ll}\text { Sasha's solution } & \text { Vanessa's solution } \\ 2^{-2} x^{2} & 2^{-2} \times 2 \\ =4^{-1} & =2^{-2} \\ =-\frac{1}{4^{1}} & =\frac{1}{2^{2}} \\ =-\frac{1}{4} & =\frac{1}{4}\end{array} </code></p><p>a) Explain where each student went wrong.</p><p>b) Write the correct solution.</p>
<p>Evaluate.</p><p><code class='latex inline'>1^5</code></p>
<p>Evaluate</p><p><code class='latex inline'> \displaystyle (-34)^0 </code></p>
<p>Write as a single power. Express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle (9^3)^6 </code></p>
<p>Evaluate using the laws of exponents.</p><p><code class='latex inline'> \displaystyle (5^0 + 5^2)^{-1} </code></p>
<p>Apply the power rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>(0.2^2)^3</code></p>
<p>Simplify. then evaluate without using a calculator.</p><p><code class='latex inline'> \displaystyle (\frac{4}{3})(\frac{4}{3})^2 </code></p>
<p>Evaluate. </p><p><code class='latex inline'> 2^ {-6}</code></p>
<p>Simplify. Write each expression as a single power with a positive exponent. <code class='latex inline'>\displaystyle 2^{4}\left(2^{2}\right) \div 2^{-6} </code></p>
<p>Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'>\displaystyle 8^{\frac{5}{2}} \div 8^{-\frac{5}{2}} </code></p>
<p>Write each expression as a single power.</p><p><code class='latex inline'> \displaystyle 6^{16} \div 6^{11} </code></p>
<p>Simplify, then determine the number that makes each statement true.</p><p><code class='latex inline'> \displaystyle (\frac{m^7}{m^6})^2 = 196 </code></p>
<p>Find the value of each expression for <code class='latex inline'>a = 1, b = 3</code>, and <code class='latex inline'>c = 2</code>.</p><p><code class='latex inline'> \displaystyle (-a \div b)^{-c} </code></p>
<p>Find the value of each expression for <code class='latex inline'>a = 1, b = 3</code>, and <code class='latex inline'>c = 2</code>.</p><p><code class='latex inline'> \displaystyle (a^{b}b^{a})^c </code></p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle \frac{6^{-5}}{(6^2)^{-2}} </code></p>
<p>Simplify, using the exponent rules. Express each answer in exponential form. </p><p><code class='latex inline'>\displaystyle y^{5} \times y^{3} \div y^{2} </code></p>
<p>Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'> \displaystyle 6^{-7} \times 6^5 </code></p>
<p>Evaluate each expression.</p><p><code class='latex inline'>\displaystyle 3.2^{2} </code></p>
<p>Write as a single power. Express answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \left(10\left(10^{3}\right)^{-1}\right)^{-2} </code></p>
<p>Evaluate. Remember to use the correct order of operations.</p><p><code class='latex inline'>(\dfrac{3}{4})^2\times (-\dfrac{2}{3})^3</code></p>
<p>Write as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>4^6 \div 4^5 \times 4^2</code></p>
<p>Simplify. Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'>\displaystyle \left(\frac{\left(5^{3}\right)^{2}}{5\left(5^{6}\right)}\right)^{-1} </code></p>
<p>Evaluate the power. Express your answer in rational form.</p><p><code class='latex inline'>\displaystyle 5^{-2} </code></p>
<p>Evaluate the power. Express your answer in rational form.</p><p> <code class='latex inline'>\displaystyle (-3)^{-4}</code> </p>
<p>Evaluate.</p><p><code class='latex inline'>\displaystyle 5^{3} </code></p>
<p>ALGEBRA Which of the following has the same value as <code class='latex inline'>\displaystyle 2^{-12} \times 2^{3} </code> ?</p><img src="/qimages/104278" />
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle 4^{3} </code></p>
<p>Evaluate.</p><p><code class='latex inline'>-1^{28}</code></p>
<p>Simplify, then determine the number that makes each statement true.</p><p><code class='latex inline'> \displaystyle (n^2)^5 \div n^5 = 243 </code></p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle \frac{(5^3)^{-2}}{5^{-6}} </code></p>
<p>Evaluate.</p><p><code class='latex inline'>(-18)^{0}</code></p>
<p>Apply the power rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>(-1^6)^3</code></p>
<p><strong>(a)</strong> Express <code class='latex inline'>\displaystyle \frac{3^3}{3^4}</code> as a single power using the division rule for exponents.</p><p><strong>(b)</strong> Rewrite the numerator and denominator of the expression <code class='latex inline'>\displaystyle \frac{3^3}{3^4}</code> in factored form. Simplify where possible. What is the value of this expression?</p>
<p>Write as a single power. Express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \left(16^{2}\right)^{5} </code></p>
<p>Evaluate each expression for <code class='latex inline'>x = -2, y = 3</code>, and <code class='latex inline'>n = -1</code>. Express answers in rational form.</p><p><code class='latex inline'>\displaystyle (\frac{x^n}{y^n})^n </code></p>
<p>Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'> \displaystyle \frac{2^8}{2^{-5}} </code></p>
<p>Evaluate each expression.</p><p><code class='latex inline'>\displaystyle (2.5)^{2} </code></p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle \frac{(12^{-1})^{3}}{12^{-3}} </code></p>
<p>Evaluate each expression. <code class='latex inline'>\displaystyle 3^{5} </code></p>
<p>Which do you think is greater: <code class='latex inline'>5^{-2}</code> or <code class='latex inline'>10^{-2}</code>? Justify your decision.</p>
<p>Evaluate each expression. <code class='latex inline'>\displaystyle 4^{2} </code></p>
<p>Evaluate. </p><p><code class='latex inline'> (-4) ^ {-2}</code></p>
<p>Evaluate using the laws of exponents.</p><p><code class='latex inline'> \displaystyle \left(\frac{3^{-1}}{2^{-1}}\right)^{-2} </code></p>
<p>Evaluate. </p><p><code class='latex inline'> (-6) ^ {-3}</code></p>
<p>Evaluate <code class='latex inline'>(-5)^2</code> and <code class='latex inline'>(-5)^3</code>. Make a conjecture about the sign of a base and how the exponent may affect the value of the power.</p>
<p>Write each as a single power. Then evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle \frac{4^{-10}(4^{-3})^6}{(4^{-4})^8} </code></p>
<p>Apply the power rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>(5^3)^2</code></p>
<p>Evaluate the expression for the given values. Express answers in rational form.</p><p><code class='latex inline'>\displaystyle \frac{2w(3w^{-2})}{(2w)^2} </code> where <code class='latex inline'>w= -3</code></p>
<p>Write as a single power. Express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle 5\left(5^{4}\right) </code></p>
<p>Evaluate</p><p>a) <code class='latex inline'>\displaystyle 4^5 </code></p><p>b) <code class='latex inline'>\displaystyle (-3)^4 </code></p><p>c) <code class='latex inline'>\displaystyle (\frac{2}{5})^3 </code></p><p>d) <code class='latex inline'>\displaystyle 1.05^8 </code></p>
<p>Apply the power rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>[(-\dfrac{5}{6})^3]^2</code></p>
<p>Simplify, then evaluate each expression. Leave answers as fractions or integers.</p><p><code class='latex inline'>\displaystyle \frac{-2\left(-2^{-3}\right)}{(-2)^{4}} </code></p>
<p>Write as a single power. Then, evaluate.</p><p><code class='latex inline'>(-2)^2 \times (-2)^3 \times (-2)</code></p>
<p>Evaluate.</p><p><code class='latex inline'> \displaystyle (\frac{2}{5})^{-2} </code></p>
<p>Apply the power rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>[(\dfrac{1}{5})^2]^2</code></p>
<p>Evaluate.</p><p><code class='latex inline'>(\frac{2}{5})^{-2}</code></p>
<p>Evaluate.</p><p><code class='latex inline'>\displaystyle 10^{-2} </code></p>
<p>Evaluate. Expression in rational form(without negative exponents).</p><p><code class='latex inline'>\displaystyle (\frac{2}{5})^{-3} </code></p>
<p>Simplify. Write each expression as a single power with a positive exponent. <code class='latex inline'>\displaystyle \frac{9^{4}\left(9^{3}\right)}{9^{12}} </code></p>
<p>Write as a single power. Express answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{\left((-8)^{6}\right)^{-2}}{\left((-8)^{-4}\right)^{3}} </code></p>
<p>Evaluate. </p><p><code class='latex inline'> 5 ^ {-2} + 5 ^ {-2}</code></p>
<p>Evaluate. </p><p><code class='latex inline'> 0 ^{-4}</code></p>
<p>Write each power in simplified form.</p><p><code class='latex inline'>27^5</code> as a base 3 power</p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle 2^{-3}(2^7) </code></p>
<p>Simplify. Write as a single power.</p><p><code class='latex inline'> \displaystyle \frac{(8^3)(8^3)^3}{8^3(8^{11})} </code></p>
<p>Evaluate without using a calculator.</p><p><code class='latex inline'>\displaystyle 4^{0}+8^{-2}-2^{-2} </code></p>
<p>Simplify, then evaluate each expression. Leave answers as fractions or integers.</p><p><code class='latex inline'>\displaystyle \frac{3^{-2}}{3^{-6}} </code></p>
<p>Evaluate each expression.</p><p><code class='latex inline'>\displaystyle 8^{2} </code></p>
<p>Evaluate. </p><p><code class='latex inline'> (-6)^{-2}</code></p>
<p>Evaluate.</p><p><code class='latex inline'>\displaystyle\frac{(-2)^{3}}{-4}</code></p>
<p>Write as a single power. Express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \left(\frac{1}{10}\right)^{6}\left(\frac{1}{10}\right)^{-4} </code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle 5^{-3} + 10^{-3} - 8(1000^{-1}) </code></p>
<p>Which do you think is less: <code class='latex inline'>(-1)^{-100}</code> or <code class='latex inline'>(-1)^{-101}</code>? Justify your decision.</p>
<p>Find the value of each expression for <code class='latex inline'>a = 1, b = 3</code>, and <code class='latex inline'>c = 2</code>.</p><p><code class='latex inline'> \displaystyle a^{c}b^{c} </code></p>
<p>Evaluate.</p><p><code class='latex inline'>\displaystyle 1.06^{5} </code></p>
<p>Evaluate.</p><p><code class='latex inline'>\displaystyle\frac{(-12)(-3)}{-6}</code></p>
<p>Write each power in simplified form.</p><p><code class='latex inline'>(\frac{1}{4})^3</code> as a base <code class='latex inline'> \displaystyle \frac{1}{2} </code> power</p>
<p>Find the value of each expression for <code class='latex inline'>a = 1, b = 3</code>, and <code class='latex inline'>c = 2</code>.</p><p><code class='latex inline'> \displaystyle (a^{-1}b^{-2})^c </code></p>
<p>Evaluate.</p><p><code class='latex inline'>\displaystyle (\frac{3}{5})^2 \div \frac{9}{10} </code></p>
<p>Rewrite the power with a positive exponent. </p><p><code class='latex inline'> 5^ {-3}</code></p>
<p>Evaluate.</p><p><code class='latex inline'>(\dfrac{3}{4})^4</code></p>
<p>what is the simplified form of each expression?</p><p><code class='latex inline'>\displaystyle 5^{2} </code></p>
<p>Simplify. Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'>\displaystyle 9^{7} \times 9^{-3} </code></p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle 10(10^4(10^{-2})) </code></p>
<p>Simplify. Write as a single power.</p><p><code class='latex inline'> \displaystyle \frac{(5^4)^2(5^5)^2}{5^2(5^{13})} </code></p>
<p>Rewrite the power with a positive exponent. </p><p><code class='latex inline'> 3 ^ {-4}</code></p>
<p>Write each as a power of 4.</p> <ul> <li><code class='latex inline'>64</code></li> </ul>
<p>Determine the value of <em>x</em> that makes each statement true. </p><p><code class='latex inline'> x^ {-2} = \dfrac{4}{9}</code></p>
<p>Evaluate without using a calculator.</p><p><code class='latex inline'>\displaystyle \left(\frac{2}{3}\right)^{-1} </code></p>
<p>Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'> \displaystyle (-9^4)^{-1} </code></p>
<p>The probability of tossing heads with a standard coin is <code class='latex inline'>\frac{1}{2}</code>, because it is one of two possible outcomes. The probability of tossing three heads in a row is <code class='latex inline'>(\frac{1}{2})^3</code> or <code class='latex inline'>\frac{1}{8}</code>.</p><p>a) What is the probability of tossing </p> <ul> <li>six heads in a row?</li> <li>12 heads in a row?</li> </ul> <p>b) Write each answer in part a) as a power of a power.</p>
<p>Write as a single power. Express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle 5 (5^4) </code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'>\displaystyle (- \frac{1}{2})^3 + 4^{-3} </code></p>
<p>Simplify in reduced fraction form.</p><p><code class='latex inline'>\displaystyle \left(\frac{5}{2}\right)^{-3} </code></p>
<p>Evaluate.</p><p><code class='latex inline'>\displaystyle(-1)^{3}</code></p>
<p>Evaluate each expression without using a calculator.</p><p><code class='latex inline'>\displaystyle (-2)^{-4} </code></p>
<p>Write each expression with base 3.</p><p><code class='latex inline'>\displaystyle 27^2 </code></p>
<p>Evaluate. </p><p><code class='latex inline'>(\dfrac{2}{3})^{-1}</code></p>
<p>Write each expression with base 2.</p><p><code class='latex inline'>\displaystyle 8^3 </code></p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle (3^{-2}(3^3))^{-2} </code></p>
<p>Simplify using the exponent laws. Then, evaluate.</p><p><code class='latex inline'>[(-5)^2]^3\div (-5)^4\times (-5)^2</code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'>\displaystyle (\frac{4}{7})^2 </code></p>
<p>Write each as a power of 4.</p> <ul> <li><code class='latex inline'>4</code></li> </ul>
<p>Evaluate the expression for the given values. Express answers in rational form.</p><p><code class='latex inline'>\displaystyle \frac{(-2x^{-2})^3(6x)^2}{2(-3x^{-1})^3} </code> where <code class='latex inline'>x= \frac{1}{2}</code></p>
<p>Evaluate the power. Express your answer in rational form.</p><p><code class='latex inline'>\displaystyle 7^{-2} </code></p>
<p>Evaluate each expression. <code class='latex inline'>\displaystyle 7^{2} </code></p>
<p>Evaluate</p><p>a) <code class='latex inline'> \displaystyle 6^0 </code></p><p>b) <code class='latex inline'> \displaystyle (-\frac{2}{5})^{-3} </code></p>
<p>Find the value of each expression for <code class='latex inline'>a = 1, b = 3</code>, and <code class='latex inline'>c = 2</code>.</p><p><code class='latex inline'> \displaystyle (b \div c)^{-a} </code></p>
<p>Simplify, then evaluate without using a calculator.</p><p><code class='latex inline'> \displaystyle \frac{9^2}{(3^2)^2} </code></p>
<p>Write each as a single power. Then evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle (\frac{(-3)^7(-3)^4}{(-3^4)^3})^{-3} </code></p>
<p>Evaluate without using a calculator.</p><p><code class='latex inline'>\displaystyle \left(n^{-7}\right)^{-2} </code></p>
<p>Simplify, using the exponent rules. Express each answer in exponential form. </p><p><code class='latex inline'>\displaystyle 3^{2} \div 3^{2} </code></p>
<p>Apply the quotient rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>3.2^5 \div 3.2^2</code></p>
<p>Evaluate</p><p><code class='latex inline'> \displaystyle 10^{-5} </code></p>
<p>Evaluate. Leave answers as fractions or integers.</p><p><code class='latex inline'>\displaystyle 4^{-2}+3^{0}-2^{-3} </code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle \frac{12^{-1}}{(-4)^{-1}} </code></p>
<p>Simplify using the exponent laws. Then, evaluate.</p><p><code class='latex inline'>4^6\div 4^3\times 4^2</code></p>
<p>Evaluate without using a calculator.</p><p><code class='latex inline'>\displaystyle \left(-\frac{2}{5}\right)^{-3} </code></p>
<p>Evaluate each power. Express your answer in rational form.</p><p><code class='latex inline'>\displaystyle (\frac{1}{2})^{2}</code></p>
<p>Find the value of each expression for <code class='latex inline'>a = 1, b = 3</code>, and <code class='latex inline'>c = 2</code>.</p><p><code class='latex inline'> \displaystyle ac^c </code></p>
<p>Apply the product rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>2.5^3\times 2.5^3</code></p>
<p>Simplify using the exponent laws. Then, evaluate.</p><p><code class='latex inline'>3^2\times 3^4\times 3^1</code></p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle \frac{4^{-10}}{(4^{-4})^3} </code></p>
<p>Evaluate <code class='latex inline'> \displaystyle [(-5)^2]^3 </code> and <code class='latex inline'> \displaystyle (-5^2)^3 </code>. Do these expressions have the same value? Justify your answer.</p>
<p>Find the value of each expression for <code class='latex inline'>a = 1, b = 3</code>, and <code class='latex inline'>c = 2</code>.</p><p><code class='latex inline'> \displaystyle (ab)^{-c} </code></p>
<p>Simplify. Write as a single power.</p><p><code class='latex inline'> \displaystyle 10(10^5)(10^3)\div(10^3)^2 </code></p>
<p>Evaluate.</p><p><code class='latex inline'>2^3</code></p>
<p>Evaluate. Leave answers as fractions or integers.</p><p><code class='latex inline'>\displaystyle 3^{-2}-9^{-1} </code></p>
<p>Write each power in simplified form.</p><p><code class='latex inline'>4^3</code> as a base 2 power</p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle (8^{-1}) (\frac{2^{-3}}{4^{-1}}) </code></p>
<p>Write <code class='latex inline'>2^8</code> as a power of a number other than 2.</p>
<p>Simplify, then evaluate without using a calculator.</p><p><code class='latex inline'> \displaystyle \frac{(10^2)^5}{100^3} </code></p>
<p>Iridium-192 is a radioactive element used for therapy in nuclear medicine. It decays to <code class='latex inline'>\dfrac{1}{2}</code>, or <code class='latex inline'> 2^{-1}</code>, of its original mass after 74 days. After 148 days, it decays to <code class='latex inline'>\dfrac{1}{4}</code>, or <code class='latex inline'>2^{-2}</code>, of its original mass. </p><p>a) What fraction remains after 222 days?</p><p>b) What fraction remains after 269 days?</p><p>c) What fraction remains after 370 days?</p><p>d) Write each fraction as a power of 2 with a negative exponent. </p>
<p>Evaluate </p><p>a) <code class='latex inline'>4^0</code></p><p>b) <code class='latex inline'>5^{-1}</code></p><p>c) <code class='latex inline'>(-3)^{-3}</code></p><p>d) <code class='latex inline'>\left(\dfrac{3}{4}\right)^{-2}</code></p>
<p>The probability of tossing tails with a standard coin is <code class='latex inline'>\frac{1}{2}</code>, because it is one of two possible outcomes. The probability of tossing four tails in a row is <code class='latex inline'>(\frac{1}{2})^4</code> or <code class='latex inline'>\frac{1}{16}</code>.</p><p>a) What is the probability of tossing</p> <ul> <li><p>9 tails in a row?</p></li> <li><p>12 tails in a row?</p></li> </ul> <p>b) Write each answer in part a) as a power of a power.</p>
<p>Evaluate each power. Express your answer in rational form.</p><p><code class='latex inline'>\displaystyle (-\frac{3}{4})^{-2}</code> </p>
<p>Write as a single power. Express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{(-8)^4}{(-8)^5} </code></p>
<p>Rewrite each expression as an equivalent expression with a positive exponent.</p><p><code class='latex inline'>\displaystyle 4^{-6} </code></p>
<p>Apply the power rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>(-4^3)^2</code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle \frac{(-5)^3(-25)^{-1}}{(-5)^{-2}} </code></p>
<p>Determine the value of <em>x</em> that makes each statement true. </p><p><code class='latex inline'>x^{-4} = \dfrac{1}{16}</code></p>
<p>Evaluate each expression.</p><p><code class='latex inline'>\displaystyle (-4.2)^{2} </code></p>
<p>Rewrite each expression as an equivalent expression with a positive exponent.</p><p><code class='latex inline'> \displaystyle \frac{7^{-2}}{8^{-1}} </code></p>
<p>Evaluate. Leave answers as fractions or integers.</p><p><code class='latex inline'>\displaystyle 12\left(4^{0}-3^{-2}\right) </code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle 16^{-1} - 2^{-2} </code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'>\displaystyle (-\frac{2}{5})^3 </code></p>
<p>Write it as a single power.</p><p><code class='latex inline'>\displaystyle \frac{7^4 \times 7^5}{(7^4)^2} </code></p>
<p>Simplify. Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'>\displaystyle -5 \times\left(-5^{4}\right)^{-3} </code></p>
<p>Evaluate.</p><p><code class='latex inline'>(-6)^3</code></p>
<p>Rewrite each expression as an equivalent expression with a positive exponent.</p><p><code class='latex inline'> \displaystyle (\frac{3}{11})^{-1} </code></p>
<p>Evaluate the expression for the given values. Express answers in rational form.</p><p><code class='latex inline'>\displaystyle \frac{8m^{-5}}{(2m)^{-3}} </code> where <code class='latex inline'>x = 4</code></p>
<p>Evaluate the power. Express your answer in rational form.</p><p><code class='latex inline'>\displaystyle 7^{-2}</code> </p>
<p>Simplify, then evaluate without using a calculator.</p><p><code class='latex inline'> \displaystyle 5^2(\frac{(5^4)^3}{5^{10}}) </code></p>
<p>Simplify, using the exponent rules. Express each answer in exponential form. </p><p><code class='latex inline'>\displaystyle 2^{3} \times 2^{4} </code></p>
<p>Simplify. Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'>\displaystyle \frac{\left(-8^{-1}\right)\left(-8^{-5}\right)}{\left(-8^{-2}\right)^{3}} </code></p>
<p>Evaluate.</p><p><code class='latex inline'>(-\dfrac{2}{3})^3</code></p>
<p>Write as a single power. Then, evaluate.</p><p> <code class='latex inline'>\frac{3^5 \times 3^3}{(3^2)^3}</code></p>
<p>Evaluate.</p><p><code class='latex inline'>3^{-1}</code></p>
<p>Simplify. Write each expression as a single power with a positive</p><p>exponent.</p><p><code class='latex inline'>\displaystyle a^{-2} \times a^{3} \times a^{4} </code></p>
<p>Evaluate using the laws of exponents.</p><p><code class='latex inline'> \displaystyle \frac{2^5}{3^{-2}} \times \frac{3^{-1}}{2^4} </code></p>
<p>Evaluate. </p><p><code class='latex inline'>\displaystyle(-3)^{2} + 9</code></p>
<p>Evaluate the power. Express your answer in rational form.</p><p><code class='latex inline'>\displaystyle 4^{-1} </code></p>
<p>Evaluate.</p><p><code class='latex inline'>\displaystyle \left(\frac{3}{4}\right)^{3} </code></p>
<p>Simplify. Write as a single power.</p><p><code class='latex inline'> \displaystyle (\frac{3(3^{11})}{13^7})^2 </code></p>
<p>Simplify. Write each expression as a single power with a positive exponent. <code class='latex inline'>\displaystyle \left(\left(7^{2}\right)^{-3}\right)^{-4} </code></p>
<p>Write as a single power. Express answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \left((-9)^{2}\right)^{5} </code></p>
<p>Evaluate each expression.</p><p><code class='latex inline'>\displaystyle \left(\frac{1}{4}\right)^{2} </code></p>
<p>Write as a single power. Express answers with positive exponents.</p><p><code class='latex inline'>\displaystyle 3^{4} \times 3^{8} \times 3 </code></p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle (9 \times 9^{-1})^{-2} </code></p>
<p>Science The concentration of hydrogen ions in household dish detergent is <code class='latex inline'>\displaystyle 10^{-12} </code>. What is the pH level of household dish detergent?</p>
<p>Write each expression as a single power.</p><p><code class='latex inline'> \displaystyle \frac{9^3}{9} </code></p>
<p>Write as a single power. Express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{8^{8}}{8^{6}} </code></p>
<p>Apply the product rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>4^3\times 4^2</code></p>
<p>Evaluate using the laws of exponents.</p><p><code class='latex inline'> \displaystyle 4^{-1}(4^2 + 4^0) </code></p>
<p>Write it as a single power.</p><p><code class='latex inline'>\displaystyle 2^3 \times 2^2 \times 2^4 </code></p>
<p>Evaluate each expression. <code class='latex inline'>\displaystyle 12^{3} </code></p>
<p>Simplify. Write each expression as a single power with a positive exponent. <code class='latex inline'>\displaystyle \frac{\left(-12^{3}\right)^{-1}}{(-12)^{7}} </code></p>
<p>Write as a single power. Express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle (\frac{1}{10})^6(\frac{1}{10})^{-4} </code></p>
<p>Evaluate. Remember to use the correct order of operations.</p><p><code class='latex inline'>4^2\times 2^4</code></p>
<p>Evaluate.</p><p>a) <code class='latex inline'>\displaystyle -(\frac{2}{3})^{-4} </code></p><p>b) <code class='latex inline'>\displaystyle -5^{-3} </code></p>
<p>Evaluate</p><p><code class='latex inline'> \displaystyle 7^{-2} </code></p>
<p>Write each expression with base 2.</p><p><code class='latex inline'>\displaystyle 4^6 </code></p>
<p>Write each as a single power. Then evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle \frac{(-2)^8}{(-2)^3} </code></p>
<p>Evaluate. </p><p><code class='latex inline'>\displaystyle\frac{(-6)(-8)}{4}</code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle \frac{(-9)^{-2}}{(3^{-1})^2} </code></p>
<p>Simplify, then evaluate each expression. Leave answers as fractions or integers.</p><p><code class='latex inline'>\displaystyle 6^{-2}\left(6^{-2}\right)^{-1} </code></p>
<p>Write as a single power. Express answers with positive exponents.</p><p><code class='latex inline'>\displaystyle 12^{-6} \times 12^{8} \times 12^{0} </code></p>
<p>Rewrite each expression as an equivalent expression with a positive exponent.</p><p><code class='latex inline'> \displaystyle -(\frac{6}{5})^{-3} </code></p>
<p>Determine the value of <em>x</em> that makes each statement true. </p><p><code class='latex inline'> x^ {-1} = \dfrac{3}{4}</code></p>
<p>Simplify. then evaluate without using a calculator.</p><p><code class='latex inline'> \displaystyle (\frac{1}{9})^4 \div (\frac{1}{9})^2 </code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle \left(-\frac{2}{3}\right)^{-1} + \left(\frac{2}{5}\right)^{-1} </code></p>
<p>Evaluate.</p><p><code class='latex inline'>8^o</code></p>
<p>Evaluate.</p><p><code class='latex inline'>-4^2</code></p>
<p>Evaluate without using a calculator.</p><p><code class='latex inline'>\displaystyle 9^{-1}-\left(3^{-1}\right)^{2} </code></p>
<p>Solve the exponential equations.</p><p><code class='latex inline'>\displaystyle P = 9000(\frac{1}{2})^8 </code></p>
<p>Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'>\displaystyle 3^{-\frac{1}{2}} \div 3^{\frac{3}{2}} </code></p>
<p>Evaluate the expression for the given values. Express answers in rational form.</p><p><code class='latex inline'>\displaystyle (6(x^{-4})^3)^{-1} </code> where <code class='latex inline'>x= -2</code></p>
<p>Evaluate each expression.</p><p><code class='latex inline'>\displaystyle (-7)^{2} </code></p>
<p>Evaluate. </p><p><code class='latex inline'> -9 ^ {0}</code></p>
<p>Simplify. Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'>\displaystyle \left(\frac{4^{-3}}{4^{-2}}\right)^{-3} </code></p>
<p>Akina won $50 000. She decides to invest <code class='latex inline'> \dfrac{1}{2}</code>, of <code class='latex inline'> 2^ {-1}</code>, of her winnings in January, then invest half of the remaining amount in February, half again in March, and so on. </p><p>a) What fraction of her money remains after four months?</p><p>b) What fraction of her money remains after eight months?</p><p>c) Write each fraction as a power of 2 with a negative exponent. </p><p>d) What amount is remaining at the end of six months?</p>
<p>Simplify. Write as a single power.</p><p><code class='latex inline'> \displaystyle (7^8)(7^5)^2 </code></p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle \frac{4+4^{-1}}{4-4^{-1}} </code></p>
<p>Apply the product rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>(-1)^{15}\times (-1)^{25}</code></p>
<p>a) Evaluate each power.</p><p><code class='latex inline'>3^1</code> <code class='latex inline'>3^2</code> <code class='latex inline'>3^3</code> <code class='latex inline'>3^4</code> <code class='latex inline'>3^5</code> <code class='latex inline'>3^6</code></p><p>b) Examine the final digit of each of your answers. What pattern do you notice?</p><p>c) Use the pattern that you found in part b) to determine the final digit in the number <code class='latex inline'>3243^{3243}</code>.</p>
<p>Write as a single power. Express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle (\frac{7^2}{7^4})^{-4} </code></p>
<p>Evaluate each expression. <code class='latex inline'>\displaystyle 11^{5} </code></p>
<p>Write each as a single power. Then evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle (-7)^3(-7)^{-4} </code></p>
<p>Simplify. Write as a single power.</p><p><code class='latex inline'> \displaystyle \frac{10(10^9)}(10^2)^3} </code></p>
<p>Find the value of each expression for <code class='latex inline'>a = 1, b = 3</code>, and <code class='latex inline'>c = 2</code>.</p><p><code class='latex inline'> \displaystyle [(b)^{-a}]^{-c} </code></p>
<p>Write each as a single power. Then evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle \frac{(5)^{-3}(5)^6}{5^3} </code></p>
<p>Evaluate.</p><p><code class='latex inline'> \displaystyle (-9)^0 </code></p>
<p>Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'> \displaystyle \frac{11^{-3}}{11^5} </code></p>
<p>Evaluate each expression. Use the fact that <code class='latex inline'>\displaystyle 2^{5}=32 </code> and <code class='latex inline'>\displaystyle 3^{4}=81 </code>.</p><p><code class='latex inline'>\displaystyle (-2)^{5} </code></p>
<p>Write each as a single power. Then evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle (11)^{9}(\frac{1}{11})^{7} </code></p>
<p>Simplify in reduced fraction form.</p><p><code class='latex inline'>\displaystyle \left(-\frac{1}{2}\right)^{-3} </code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'>\displaystyle 4^{-2} - 8^{-1} </code></p>
<p>Simplify, using the exponent rules. Express each answer in exponential form. </p><p><code class='latex inline'>\displaystyle 3^{2} \times 3^{4} \times 3 </code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle -(6)^{-2} </code></p>
<p>Evaluate. </p><p><code class='latex inline'> (-\dfrac{5}{7})^{-3}</code></p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle \frac{5^{-2}-5^{-1}}{5^{-2}+5^{-1}} </code></p>
<p>Evaluate without using a calculator.</p><p><code class='latex inline'>\displaystyle 5^{-2}+10^{-1} </code></p>
<p>Evaluate using the laws of exponents.</p><p><code class='latex inline'> \displaystyle 2^3 \times 4^{-2} \div 2^2 </code></p>
<p>Evaluate without using a calculator.</p><p><code class='latex inline'>\displaystyle \left[\left(2^{2}\right)\left(4^{2}\right)\right]^{-1} </code></p>
<p>Simplify, using the exponent rules. Express each answer in exponential form. </p><p><code class='latex inline'>\displaystyle m^{7} \div m^{4} </code></p>
<p>Simplify. Write as a single power.</p><p><code class='latex inline'> \displaystyle \frac{(8^2)^5}{8^8} </code></p>
<p>Write as a single power. Express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{3\cdot 3^6}{3^5} </code></p>
<p>Evaluate the power. Express your answer in rational form.</p><p><code class='latex inline'>\displaystyle 8^{0} </code></p>
<p>Write each power in simplified form.</p><p><code class='latex inline'>(-8)^4</code> as a base -2 power</p>
<p>Write it as a single power.</p><p><code class='latex inline'>\displaystyle 6^7 \div 6^2 \div 6^3 </code></p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle \left(\frac{2^{2}}{2^{3}}\right)^{5} </code></p>
<p>Rewrite the power with a positive exponent. </p><p><code class='latex inline'> (-5) ^ {-1}</code></p>
<p>Evaluate. </p><p><code class='latex inline'> 7 ^ {0}</code></p>
<p>Use the division property of exponents to show why <code class='latex inline'> 0^{0} </code> is undefined.</p>
<p>Evaluate using the laws of exponents.</p><p><code class='latex inline'> \displaystyle (2 \times 3)^{-1} </code></p>
<ul> <li>Express <code class='latex inline'>\displaystyle \frac{5^2}{5^4}</code> as a single power using the division rule for exponents.</li> <li>Rewrite the numerator and denominator of the expression <code class='latex inline'>\displaystyle \frac{5^2}{5^4}</code> in factored form. Simplify where possible. What is the value of this expression?</li> </ul>
<p>Evaluate</p><p><code class='latex inline'> \displaystyle -(\frac{1}{6})^{-2} </code></p>
<p>Evaluate the power. Express your answer in rational form.</p><p><code class='latex inline'>\displaystyle (2)^{-4} </code></p>
<p>Simplify. Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'>\displaystyle \left(\left(7^{2}\right)^{-3}\right)^{-4} </code></p>
<p>Evaluate.</p><p><code class='latex inline'>(-4)^2</code></p>
<p>Write as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>5^6 \div 5 \div 5^2</code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle (-3)^{-1} + 4^0 - 6^{-1} </code></p>
<p>Apply the quotient rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>(-\dfrac{2}{5})^5 \div (-\dfrac{2}{5})^3</code></p>
<p>Evaluate.</p><p><code class='latex inline'>(-3)^{-2}</code></p>
<p>Simplify using the exponent laws. Then, evaluate.</p><p><code class='latex inline'>(6^2)^5\times (6^3)^5\div (6^5)^3</code></p>
<p>Write as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>[(-3)^2]^3</code></p>
<p>Write as a single power. Express answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{\left(20^{-1}\right)^{8}}{20^{2} 20^{6}} </code></p>
<p>Evaluate.</p><p><code class='latex inline'>(\frac{4}{3})^{-1}</code></p>
<p>Simplify. Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'>\displaystyle \left(\frac{9^{-2}}{\left(9^{2}\right)^{2}}\right)^{2} </code></p>
<p>Evaluate. </p><p><code class='latex inline'> (\dfrac{1}{4}) ^ {-2}</code></p>
<p>Rewrite each expression as an equivalent expression with a positive exponent.</p><p><code class='latex inline'>\displaystyle -(-4)^{-3} </code></p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle 9^7(9^3)^{-2} </code></p>
<p>Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'>\displaystyle 2^{0.5} \times 2^{2} \times 2^{2.5} </code></p>
<p>Rewrite each expression as an equivalent expression with a positive exponent.</p><p><code class='latex inline'>\displaystyle (-3)^{-2} </code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle 5^2(-10)^{-4} </code></p>
<p>Evaluate each expression without using a calculator.</p><p><code class='latex inline'>\displaystyle \left(\frac{3}{2}\right)^{-3} </code></p>
<p>Evaluate.</p><p><code class='latex inline'>8^{-1}</code></p>
<p>Evaluate each expression. <code class='latex inline'>\displaystyle 14^{3} </code></p>
<p>Evaluate. </p><p><code class='latex inline'> -(-10)^{0}</code></p>
<p>Evaluate the power. Express your answer in rational form.</p><p><code class='latex inline'>\displaystyle(-2)^{-5}</code> </p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle \left(\frac{1}{2}\right)^{4} </code></p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle 13^{-5} \times \left(\frac{13^2}{13^8}\right)^{-1} </code></p>
<p>Karen was asked to simplify the expression <code class='latex inline'>3^2 (2^2)^2</code>. This is her solution:</p><p><code class='latex inline'> \displaystyle 3^2(2^2)^2 = 3^2(2^4) = 6^6 = 46456 </code></p><p>Her solution is incorrect.</p><p>a) Identify her error.</p><p>b) Determine the correct answer. Show your steps.</p>
<p>Rewrite each expression as an equivalent expression with a positive exponent.</p><p><code class='latex inline'>\displaystyle -(-5)^{-2} </code></p>
<p>Evaluate the expression for the given values. Express answers in rational form.</p><p><code class='latex inline'>\displaystyle \frac{(9y)^2}{(3y^{-1})^3} </code> where <code class='latex inline'>y= -2</code></p>
<p>Write as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>\dfrac{(5^4)^3}{5^5 \times 5^4}</code></p>
<p>Write it as a single power.</p><p><code class='latex inline'>\displaystyle [(-4)^2]^3 </code></p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle 7^{4} </code></p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle (4^{-3})^{-1} </code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'>\displaystyle 25^{-1} + 3(5^{-1})^2 </code></p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle 8(8^2)(8^{-4}) </code></p>
<p>Evaluate the power. Express your answer in rational form.</p><p><code class='latex inline'>\displaystyle 5^{-2}</code> </p>
<p>Simplify</p><p><code class='latex inline'>\displaystyle \frac{n^5 \times n^3}{n^4} </code></p>
<p>Evaluate.</p><p><code class='latex inline'> \displaystyle -5^{-1} </code></p>
<p>Evaluate. </p><p><code class='latex inline'> (8-5) ^ {0}</code></p>
<p>Rewrite each expression as an equivalent expression with a positive exponent.</p><p><code class='latex inline'> \displaystyle (-\frac{1}{10})^{-3} </code></p>
<p>Apply the quotient rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>(-5)^4 \div (-5)</code></p>
<p>Simplify. Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'>\displaystyle \left(\frac{10}{10^{-3}}\right)^{2}\left(\frac{10^{5}}{10^{7}}\right) </code></p>
<p>Which is the greater power, <code class='latex inline'>2^{-5}</code> or <code class='latex inline'>(\frac{1}{2})^{-5}</code>? Explain.</p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle (a^3)^4 </code></p>
<p>Simplify. Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'>\displaystyle \frac{\left(-12^{3}\right)^{-1}}{(-12)^{7}} </code></p>
<p>Simplify using the exponent laws. Then, evaluate.</p><p><code class='latex inline'>\dfrac{(-3)^5\div (-3)^2}{(-3)^2}</code></p>
<p>Evaluate. Leave answers as fractions or integers.</p><p><code class='latex inline'>\displaystyle \frac{4^{2}}{2^{5}} </code></p>
<p>Explain the difference between evaluating <code class='latex inline'>(-10)^{4}</code> and evaluating <code class='latex inline'>-10^{4}</code>.</p>
<p>Apply the product rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>(\dfrac{2}{3})^4\times (\dfrac{2}{3})^3</code></p>
<p>Evaluate. Remember to use the correct order of operations.</p><p><code class='latex inline'>2^6\div 4^3</code></p>
<p>Evaluate. </p><p><code class='latex inline'> (5+5) ^ {-2}</code></p>
<p>Evaluate each power. Express your answer in rational form.</p><p><code class='latex inline'>\displaystyle -(\frac{3}{4})^{-2}</code> </p>
<p>Evaluate.</p><p><code class='latex inline'>25^{0}</code></p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle \frac{5^4}{5^6} </code></p>
<p>Rewrite the numerator and denominator of the expression <code class='latex inline'>\displaystyle \frac{3^4}{3^4}</code> in factored form. Simplify where possible. What is the value of this expression?</p>
<p>Evaluate the power. Express your answer in rational form.</p><p><code class='latex inline'>\displaystyle -4^{-2}</code> </p>
<p>Rewrite each expression as an equivalent expression with a positive exponent.</p><p><code class='latex inline'> \displaystyle 5^{-4} </code></p>
<p>Evaluate each power. Express your answer in rational form.</p><p><code class='latex inline'>\displaystyle (\frac{2}{3})^{-3}</code> </p>
<p>Write each power in simplified form.</p><p><code class='latex inline'>(\frac{1}{25})^4</code> as a base <code class='latex inline'> \displaystyle \frac{1}{5} </code> power</p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'>\displaystyle (\frac{-2}{3})^{-3} </code></p>
<p>Consider the following powers: <code class='latex inline'> 2^{12}, 4^{6}, 8^{4}, 16^{3} </code> </p><p>a) Use your calculator to show that the powers above are equivalent.</p><p>b) Can you think of a way to explain why each power above is equivalent to the preceding power without referring to your calculator?</p><p>c) Create a similar list using 3 as the base.</p>
<p>Rewrite each expression as an equivalent expression with a positive exponent.</p><p><code class='latex inline'>\displaystyle \frac{1}{2^{-4}} </code></p>
<p>Determine the number of digits in the expansion of <code class='latex inline'>(2^{120})(5^{125})</code> without using a calculator or computer.</p>
<p>Evaluate. Leave answers as fractions or integers.</p><p><code class='latex inline'>\displaystyle \left(\frac{1}{2}\right)^{-1}+\left(\frac{1}{3}\right)^{-1} </code></p>
<p>Rewrite the power with a positive exponent. </p><p><code class='latex inline'> 10 ^{-5}</code></p>
<p>Write as a single power. Express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \left(\frac{(7)^{2}}{(7)^{4}}\right)^{-5} </code></p>
<p>Evaluate each expression. <code class='latex inline'>\displaystyle 4^{4} </code></p>
<p>Write each expression with base 2.</p><p><code class='latex inline'>\displaystyle (\frac{1}{8})^2 </code></p>
<p>Evaluate.</p><p><code class='latex inline'>2.3^3</code></p>
<p>Evaluate. Leave answers as fractions or integers.</p><p><code class='latex inline'>\displaystyle 8^{-2}+\left(4^{-1}\right)^{2} </code></p>
<p>Simplify. Write each expression as a single power with a positive exponent. <code class='latex inline'>\displaystyle -5 \times\left(-5^{4}\right)^{-3} </code></p>
<p>Simplify. Write each expression as a single power with a positive exponent. <code class='latex inline'>\displaystyle \frac{11^{-2}\left(11^{3}\right)}{\left(11^{-2}\right)^{4}} </code></p>
<p>Determine the value of <em>x</em> that makes each statement true. </p><p><code class='latex inline'> x^ {-3} = \dfrac{1}{64}</code></p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle \left(\frac{(-4)^{2}}{(-3)^{-3}}\right)^{2} </code></p>
<p>Evaluate each expression for <code class='latex inline'>x = -2, y = 3</code>, and <code class='latex inline'>n = -1</code>. Express answers in rational form.</p><p><code class='latex inline'>\displaystyle (\frac{xy^n}{(xy)^{2n}})^{2n} </code></p>
<p>Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'>\displaystyle 2^{3} \times 4^{-2} \div 8 </code></p>
<p>Write as a single power. Express answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{(-5)^{6}}{(-5)^{4}} </code></p>
<p>Evaluate using the laws of exponents.</p><p><code class='latex inline'>\displaystyle \frac{3^{-2} \times 2^{-3}}{3^{-1} \times 2^{-2}} </code></p>
<p>Evaluate each expression without using a calculator.</p><p><code class='latex inline'>\displaystyle 5^{-3} </code></p>
<p>Without using your calculator, write the given numbers in order from least to greatest. </p><p><code class='latex inline'>\displaystyle (0.1)^{-1}, 4^{-1}, 5^{-2}, 10^{-1}, 3^{-2}, 2^{-3} </code></p>
<p>Evaluate. </p><p><code class='latex inline'> -3 ^ {-2}</code></p>
<p>Calculate. </p><p><code class='latex inline'>(\frac{2}{3})^3</code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle 16^{-1}(2^5) </code></p>
<ul> <li>Express <code class='latex inline'>\displaystyle \frac{5^2}{5^5}</code> as a single power using the division rule for exponents.</li> <li>Rewrite the numerator and denominator of the expression <code class='latex inline'>\displaystyle \frac{5^2}{5^5}</code> in factored form. Simplify where possible. What is the value of this expression?</li> </ul>
<p>Simplify, using the exponent rules. Express each answer in exponential form. </p><p><code class='latex inline'>\displaystyle 2^{5} \div 2^{3} </code></p>
<p>Express <code class='latex inline'>\displaystyle \frac{3^4}{3^4}</code> as a single power using the division rule for exponents.</p>
<p>Evaluate. </p><p><code class='latex inline'> 8 ^ {-1}</code></p>
<p>Rewrite each expression as an equivalent expression with a positive exponent.</p><p><code class='latex inline'>\displaystyle (-4)^{-3} </code></p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle 3^3(3^2)^{-1} </code></p>
<p>Express <code class='latex inline'>\displaystyle \frac{5^3}{5^3}</code>as a single power using the division rule for exponents then evaluate.</p>
<p>Evaluate each power. Express your answer in rational form.</p><p><code class='latex inline'>\displaystyle (\frac{1}{2})^{-2}</code> </p>
<p>Apply the quotient rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>8^5 \div 8^3</code></p>
<p>Evaluate.</p><p><code class='latex inline'>(-2)^{-5}</code></p>
<p>Evaluate.</p><p><code class='latex inline'>\displaystyle 3^2 + 2^3 </code></p>
<p>Apply the product rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>(-2)^2\times (-2)^4</code></p>
<p>If <code class='latex inline'> x=-2 </code> and <code class='latex inline'> y=3 </code> , write the following three expressions in order from least to greatest.</p><p><code class='latex inline'>\displaystyle \frac{y^{-4}\left(x^{2}\right)^{-3} y^{-3}}{x^{-5}\left(y^{-4}\right)^{2}}, \frac{x^{-3}\left(y^{-1}\right)^{-2}}{\left(x^{-5}\right)\left(y^{4}\right)},(y-5)\left(x^{5}\right)-2\left(y^{2}\right)(x-3)-4 </code></p>
<p>Evaluate</p><p><code class='latex inline'> \displaystyle (-7)^{-2} </code></p>
<p>Write a verbal expression for each algebraic expression.</p><p><code class='latex inline'>\displaystyle r^{4} \cdot t^{3} </code></p>
<p>Rewrite each expression as an equivalent expression with a positive exponent.</p><p><code class='latex inline'>\displaystyle (-4)^{-2} </code></p>
<p>Simplify using the exponent laws. Then, evaluate.</p><p><code class='latex inline'>4^5\div 4^2\div 4</code></p>
<p>Evaluate. </p><p><code class='latex inline'> 3 ^ {-2}</code></p>
<p>Write as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>4^6 \div 4^5 \times 4^2</code></p>
<p>Evaluate. </p><p><code class='latex inline'>\displaystyle(5)^{3} \times (-4)</code></p>
<p>Evaluate without using a calculator.</p><p><code class='latex inline'>\displaystyle \left(6^{-2}\right)^{-1}+\left(\frac{1}{3}\right)^{-2} </code></p>
<p>Kendra, Eric and Vince are studying. They wish to evaluate <code class='latex inline'>3^{-2} \times 3</code>. Kendra notices errors in each of her firends&#39; solutions, shown here.</p><p><strong>Eric&#39;s Solution</strong></p><p><code class='latex inline'>\displaystyle \begin{array}{lll} & 3^{-2} \times 3 \\ =&3^{-1} \\ =&- \frac{1}{3^{1}} \\ =&- \frac{1}{3} \\ \end{array} </code></p><p><strong>Vince&#39;s Solution</strong></p><p><code class='latex inline'>\displaystyle \begin{array}{lll} & 3^{-2} \times 3 \\ =&3^{-2} \\ =& \frac{1}{3^{2}} \\ =&\frac{1}{9} \\ \end{array} </code></p><p>a) Explain where each student went wrong.</p><p>b) Create a solution that demonstrates the correct steps.</p>
<p>Simplify, using the exponent rules. Express each answer in exponential form. </p><p><code class='latex inline'>\displaystyle -20 a^{4} \div\left(-5 a^{2}\right) </code></p>
<p>Simplify, then evaluate each expression. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle \frac{3^{-8}}{3^{-6}} </code></p>
<p>Simplify. Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'>\displaystyle \left(\frac{3^{4}}{3^{6}}\right)^{-1} </code></p>
<p>Evaluate.</p><p><code class='latex inline'>2^{-4}</code></p>
<p>Apply the product rule to write each as a single power. Then, evaluate the expression.</p><p><code class='latex inline'>(-\dfrac{3}{5})^2\times (-\dfrac{3}{5})^3</code></p>
<p>Evaluate each power. Express your answer in rational form.</p><p><code class='latex inline'>\displaystyle (\frac{2}{3})^3</code> </p>
<p>Evaluate. </p><p><code class='latex inline'> 5 ^ {-3}</code></p>
<p>Write as a single power. Express answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{4^{7} 4^{5}}{4^{12}} </code></p>
<p>Simplify, then evaluate each expression. Leave answers as fractions or integers.</p><p><code class='latex inline'>\displaystyle \left(\frac{10^{-3}}{10^{-5}}\right)^{2} </code></p>
<p>Evaluate each expression. <code class='latex inline'>\displaystyle 2^{6} </code></p>
<p>Write each expression as a single power with a positive exponent.</p><p><code class='latex inline'>\displaystyle 4^{0.3} \div 4^{0.8} \times 4^{-0.7} </code></p>
<p>Calculate. </p><p><code class='latex inline'>(\frac{3}{5})^2</code></p>
<p>Write each expression as a single power with positive exponents.</p><p><code class='latex inline'>\displaystyle 4^{\frac{2}{3}} \div 4^{\frac{-1}{2}} \times 4^{\frac{5}{6}} </code></p>
<p>Simplify. The first part has been done for you.</p><p><code class='latex inline'>\displaystyle \frac{3}{16} \times 2 </code></p>
<p>Carbon-14 is a radioactive material that is used for the dating of materials. It decays to <code class='latex inline'>\dfrac{1}{2}</code>, or <code class='latex inline'>2^{-1}</code>, of its original mass after every 5730 years. Determine the remaining mass of 0.8 kg of carbon-14 after</p><p>a) 11 460 years </p><p>b) 17 190 years</p>
<p>Evaluate each expression for <code class='latex inline'>x = -2, y = 3</code>, and <code class='latex inline'>n = -1</code>. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle (x^n + y^n)^{-2n} </code></p>
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