5. Q5a
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Similar Question 1
<p> Simplify the expression as much as possible. State the final answer without any negative exponents. <code class='latex inline'> \displaystyle \frac{9^{-2} \times 3^4}{12^{-4}} </code></p>
Similar Question 2
<p>Determine the value of x that makes each statement true.</p><p><code class='latex inline'> \displaystyle 2^x = \frac{1}{4} </code></p>
Similar Question 3
<p>Verify that <code class='latex inline'> \displaystyle (-4)^{-2} = \frac{1}{(-4)^2} </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>A positive exponent shows repeated multiplication. What repeated operation does a negative exponent show?</p>
<p>Rewrite each power with a positive exponent.</p><p><code class='latex inline'> \displaystyle 10^{-4} </code></p>
<p>The number of bees in a hive is 1000 on June 1 and doubles every month. This can be expressed as <code class='latex inline'>N=1000 \times 2^t</code>, where N represents the number of bees and t represents time, in months.</p> <ul> <li>Is it possible for <code class='latex inline'>t</code> to be -1? What does this mean?</li> </ul>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle 2^{-5} </code></p>
<p>Determine the value of x that makes each statement true.</p><p><code class='latex inline'> \displaystyle (\frac{2}{5})^x = \frac{125}{8} </code></p>
<p>Calculate</p><p><code class='latex inline'>\displaystyle -4^2 - (-4)^2 - 4^2 </code></p>
<p>Evaluate using pencil and paper. Check your results using a calculator.</p><p><code class='latex inline'> \displaystyle 6^0 + 6^{-2} </code></p>
<p>Evaluate each expression for <code class='latex inline'> a=2 </code> and <code class='latex inline'> b=-4 </code> .</p><p><code class='latex inline'>\displaystyle a^{3} b^{-1} </code></p>
<p>Solve each equation for <code class='latex inline'>x</code>.</p><p><code class='latex inline'> \displaystyle 3^x = \frac{1}{81} </code></p>
<p>Rewrite each power with a positive exponent.</p><p><code class='latex inline'> \displaystyle 3^{-2} </code></p>
<p>Evaluate. Express answers as rational numbers.</p><p><code class='latex inline'>\displaystyle (-5)^{-3} </code></p>
<p>Determine the value of x that makes each statement true.</p><p><code class='latex inline'> \displaystyle 2^x = \frac{1}{4} </code></p>
<p>Calculate</p><p><code class='latex inline'>\displaystyle \begin{array}{llll} &(a) & -2(-2)^3 & &(b) & -2^2(-2)^3 \end{array} </code></p>
<p>What is the value(or simplified answer) of <code class='latex inline'>-b^n + (-b)^n</code> if </p><p>a) <code class='latex inline'>n</code> is even</p><p>b) <code class='latex inline'>n</code> is odd</p>
<p>Evaluate.</p><p><code class='latex inline'> \displaystyle 6^{-2} </code></p>
<p>Evaluate.</p><p><code class='latex inline'> \displaystyle (-\frac{1}{4})^{-1} </code></p>
<p> Simplify the expression as much as possible. State the final answer without any negative exponents. <code class='latex inline'> \displaystyle \frac{8^{-3} \times 7^{-3} \times 5^{-4}}{40^{-10}} </code></p>
<p> Iodine-123 is a radioactive element used in medical imaging. It decays to <code class='latex inline'>\frac{1}{2}</code> of its original mass after 13 h. After 26 h, it decays to <code class='latex inline'>\frac{1}{4}</code>, or <code class='latex inline'>2^{-2}</code>, of its original mass. intercepts.</p> <ul> <li>What fraction remains after 78 h?</li> </ul>
<p> Simplify the expression as much as possible. State the final answer without any negative exponents. <code class='latex inline'> \displaystyle \frac{9^{-2} \times 3^4}{12^{-4}} </code></p>
<p>Evaluate.</p><p><code class='latex inline'> \displaystyle 7^{-1} </code></p>
<p>Calculate</p><p><code class='latex inline'>\displaystyle -8^2 - 2(-4)^3 </code></p>
<p>Evaluate.</p><p><code class='latex inline'> \displaystyle 0^{-5} </code></p>
<p>Calculate</p><p><code class='latex inline'>\displaystyle \begin{array}{lllll} &(a) & (-\frac{2}{3})^3 & &(b) & (\frac{-2}{3})^3 \\ & (c)& (\frac{2}{-3})^3 \\ \end{array} </code></p>
<p>Verify that <code class='latex inline'> \displaystyle (-4)^{-2} = \frac{1}{(-4)^2} </code></p>
<p> Expand the following so that it contains only <strong>prime</strong> base. First determine if each question is positive or negative then simplify the exponents.</p><p><code class='latex inline'>\displaystyle (-6)^4 \times 8^2 </code></p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle 3 \cdot 10^{-3} </code></p>
<p>Determine the value of x that makes each statement true.</p><p><code class='latex inline'> \displaystyle x^{-1} = \frac{4}{5} </code></p>
<p> Expand the following so that it contains only <strong>prime</strong> base. First determine if each question is positive or negative then simplify the exponents.</p><p><code class='latex inline'>\displaystyle 8^4 \times (-4)^3 </code></p>
<p>Evaluate.</p><p><code class='latex inline'> \displaystyle (\frac{1}{3})^{-2} </code></p>
<p> Simplify the expression as much as possible. State the final answer without any negative exponents. <code class='latex inline'> \displaystyle \frac{-2^{-3} \times 3^6}{-12^{-10}} </code></p>
<p>Evaluate.</p><p><code class='latex inline'> \displaystyle (-12)^{-2} </code></p>
<p>Evaluate.</p><p><code class='latex inline'> \displaystyle (\frac{9}{4})^{-3} </code></p>
<p> Iodine-123 is a radioactive element used in medical imaging. It decays to <code class='latex inline'>\frac{1}{2}</code> of its original mass after 13 h. After 26 h, it decays to <code class='latex inline'>\frac{1}{4}</code>, or <code class='latex inline'>2^{-2}</code>, of its original mass. intercepts.</p> <ul> <li>What fraction remains after 52 h?</li> </ul>
<p>Determine the value of x that makes each statement true.</p><p><code class='latex inline'> \displaystyle x^{-3} = \frac{1}{27} </code></p>
<p>Uranium-238 is a radioactive element found in rocks and many types of soils. Uranium-238 decays to <code class='latex inline'>\frac{1}{2}</code>, or <code class='latex inline'>2^{-1}</code>, of its original amount after every 4.5 billion years. Determine the remaining mass of 0.5 kg or uranium-238 after </p> <ul> <li>9 billion years</li> </ul>
<p>Fill in the blank with <code class='latex inline'><, ></code> or <code class='latex inline'>=</code> symbol to make it true.</p><p><code class='latex inline'> \begin{array}{ccc} &(a) (-6)^4 \bigcirc -6^4 & &(b) -(8^4) \bigcirc (-8)^4 \\ &(c) (-12)^3 \bigcirc (-12^3) & &(d) (-15)^4 \bigcirc 15^4 \\ \end{array} </code></p>
<p>Evaluate each expression for <code class='latex inline'> a=2 </code> and <code class='latex inline'> b=-4 </code> .</p><p><code class='latex inline'>\displaystyle 2 a^{-4} b^{0} </code></p>
<p>Evaluate.</p><p><code class='latex inline'> \displaystyle 10^{-3} </code></p>
<p>Rewrite each power with a positive exponent.</p><p><code class='latex inline'> \displaystyle 5^{-1} </code></p>
<p> Iodine-123 is a radioactive element used in medical imaging. It decays to <code class='latex inline'>\frac{1}{2}</code> of its original mass after 13 h. After 26 h, it decays to <code class='latex inline'>\frac{1}{4}</code>, or <code class='latex inline'>2^{-2}</code>, of its original mass. intercepts.</p> <ul> <li>Write each fraction as a power of 2 with a negative exponent.</li> </ul>
<p>Evaluate.</p><p><code class='latex inline'> \displaystyle (-9)^{-1} </code></p>
<p>Rewrite each power with a positive exponent.</p><p><code class='latex inline'> \displaystyle 7^{-3} </code></p>
<p>Evaluate.</p><p><code class='latex inline'> \displaystyle (\frac{5}{6})^{-2} </code></p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle \left(\frac{2}{5}\right)^{-1} </code></p>
<p>Rewrite each power with a positive exponent.</p><p><code class='latex inline'> \displaystyle (-2)^{-4} </code></p>
<p>Rewrite each power with a positive exponent.</p><p><code class='latex inline'> \displaystyle (-7)^{-1} </code></p>
<p>Evaluate.</p><p><code class='latex inline'> \displaystyle (-\frac{3}{8})^{-4} </code></p>
<p>Simplify using the laws of exponents.</p><p><code class='latex inline'>\displaystyle 5^{-3} + 10^{-3} - 8(1000^{-1}) </code></p>
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