6. Q6a
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Similar Question 1
<p>Simplify.</p><p><code class='latex inline'>\displaystyle 24 k^5 q^3 \div (2k^q)^2 </code></p>
Similar Question 2
<p>Simplify and state any restrictions.</p><p><code class='latex inline'>\displaystyle \frac{3x}{32y} \div \frac{27x^2}{96y} </code></p>
Similar Question 3
<p>Multiply. </p><p><code class='latex inline'>\displaystyle \left(8 r^{3} s^{2} t\right)\left(4 s^{3} t\right) </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>Simplify and express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{(4r^{-6})(-2r^2)^5}{(-2r)^4} </code></p>
<p>Simplify. Assume that no denominator equals zero.</p><p><code class='latex inline'>\displaystyle \frac{18 a^{2} b}{9 a b} </code></p>
<p>Multiply. </p><p><code class='latex inline'>\displaystyle \left(-6 m^{2} n^{3}\right)\left(-7 m n^{2}\right) </code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'>\displaystyle \frac{(-3)^{-2}}{(-3)^{-5}} </code></p>
<p>Simplify. Write the expression using only positive exponents. All variables are positive.</p><p><code class='latex inline'>\displaystyle \sqrt{\frac{a^6b^5}{a^8b^3}} </code></p>
<p>Simplify.</p><p><code class='latex inline'>x^5\times x^3</code></p>
<p>Simplify. Express each answer with positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{a^{-4}}{a^{-2}} </code></p>
<p>Simplify. Assume that no denominator equals zero.</p><p><code class='latex inline'>\displaystyle \frac{-40 x^{3} y^{4} z^{2}}{8 x^{3} y^{3}} </code></p>
<p>Multiply. </p><p><code class='latex inline'>\displaystyle (2 x y)\left(-3 x^{2} y^{3}\right)\left(-3 x^{2}\right) </code></p>
<p>Compare and contrast the property for raising a power to a power and the property for multiplying powers with the same base.</p>
<p>Simplify. Express each answer with positive exponents.</p><p><code class='latex inline'>\displaystyle \left(y^{3}\right)^{2} </code></p>
<p>Simplify.</p><p><code class='latex inline'>\dfrac{d^6 \times d^5}{d^7}</code></p>
<p>Simplify. State any restrictions on the variables.</p><p><code class='latex inline'> \displaystyle \frac{6x^2y}{5y^3} \times \frac{xy}{8} </code></p>
<p>Simplify</p><p><code class='latex inline'>\displaystyle \frac{2ab^2 \times 3a^3b^3}{(4ab^2)^2} </code></p>
<p>Simplify, using the exponent rules. Express each answer in exponential form. </p><p><code class='latex inline'>\displaystyle \left(2 x^{2}\right)^{3} </code></p>
<p>Simplify.</p><p><code class='latex inline'>\dfrac{(y^6)^3}{(y^5)^2}</code></p>
<p>Simplify.</p><p><code class='latex inline'>\dfrac{33x^5y^7\div 11xy^2}{12x^5y^3\div 4x^2y^2}</code></p>
<p>Simplify. Express your answer with positive exponents only.</p><p><code class='latex inline'>\displaystyle (x^{-3})^{-3}(x^{-1})^5 </code></p>
<p>Wind Energy The power generated by a wind turbine depends on the wind speed. The expression <code class='latex inline'>\displaystyle 800 v^{3} </code> gives the power in watts for a certain wind turbine at wind speed <code class='latex inline'>\displaystyle v </code> in meters per second. If the wind speed triples, by what factor does the power generated by the wind turbine increase?</p>
<p>Simplify. Assume that no denominator equals zero.</p><p><code class='latex inline'>\displaystyle \frac{-27 a^{2} b c^{4}}{-3 a b c^{2}} </code></p>
<p>Consider the expression <code class='latex inline'>\displaystyle \frac{5xy^2 \times 2x^2 y}{(2xy)^2} </code>.</p><p>a) Substitute x = and y = -1 in to the expression. Then, evaluate the expression.</p><p>b) Simplify the original expression using the exponent laws.</p><p>c) Describe the advantages and disadvantages of each method.</p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'>\displaystyle (4 + 8)^0 -5^{-2} </code></p>
<p>Simplify. State any restrictions on the variables.</p><p><code class='latex inline'> \displaystyle \frac{2x^3y}{3xy^2} \times \frac{9x}{4x^2y} </code></p>
<p><code class='latex inline'>\displaystyle 3^{x+2}=27^{2 x} </code></p>
<p>Simplify.</p><p><code class='latex inline'>a^3b\times ab^3</code></p>
<p>Simplify.</p><p><code class='latex inline'>3x^3y^2\times 5x^4y^3</code></p>
<p>Simplify, using the exponent rules. Express each answer in exponential form. </p><p><code class='latex inline'>\displaystyle 2 y^{2} \times 4 y^{3} </code></p>
<p>Simplify each algebraic expression.</p><p><code class='latex inline'>\displaystyle \frac{14 x^{7} y^{9}}{7 x^{4} y^{6}} </code></p>
<p><code class='latex inline'>\displaystyle 5^{3 x}=\frac{1}{125} </code></p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle \left(4 x^{3}\right)\left(-5 x^{3}\right)\left(-6 x^{3}\right) </code></p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle n^{5 x} \div n^{x} </code></p>
<p>Simplify. State any restrictions on the variables.</p><p><code class='latex inline'> \displaystyle \frac{3a^2b^3}{2ab^2} \div \frac{9a^2b}{14a^2} </code></p>
<p>Error Analysis A student incorrectly simplified <code class='latex inline'> \frac{x^{n}}{a^{-n} b^{0}} </code> as shown below. Find and correct the student&#39;s error.</p><p><code class='latex inline'>\displaystyle \frac{x^{n}}{a^{-n} b^{0}}=\frac{a^{n} x^{n}}{b^{0}}=\frac{a^{n} x^{n}}{0} </code> undefined</p>
<p>Express each quotient as a product by using negative exponents.</p><p><code class='latex inline'>\displaystyle \frac{(9-x^2)^3}{(2x + 1)^4} </code></p>
<p>Simplify each algebraic expression.</p><p><code class='latex inline'>\displaystyle \frac{3 a b c}{9 b} </code></p>
<p>Simplify</p><p><code class='latex inline'>\displaystyle cd^3 \times c^4 d^2 </code></p>
<p>Multiply.</p><p><code class='latex inline'>\displaystyle \left(-4 r s^{3} t^{2}\right)\left(-6 r s t^{4}\right) </code></p>
<p>Simplify. State any restrictions on the variables.</p><p><code class='latex inline'> \displaystyle \frac{7a}{3} \div \frac{14a^2}{5} </code></p>
<p>Simplify and express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle (3a^2)^{-3}(9a^{-1})^2 </code></p>
<p><code class='latex inline'>\displaystyle 8+10^{x}=1008 </code></p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle (a^{10 + 2p})(a^{-p-8}) </code></p>
<p>Simplify and express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle (\frac{2abc^3}{(2a^2b^3c)^2})^{-2} </code></p>
<p>Evaluate. Express answers in rational form.</p><p><code class='latex inline'> \displaystyle 3^{-2} - 6^{-2} + \frac{3}{2}(-9)^{-1} </code></p>
<p>Simplify. Express each answer with positive exponents.</p><p><code class='latex inline'>\displaystyle \left(k^{6}\right)^{-2} </code></p>
<p><code class='latex inline'>\displaystyle 12^{y-2}=20 </code></p>
<p>Simplify each algebraic expression.</p><p><code class='latex inline'>\displaystyle \frac{20 x}{5 x^{3}} </code></p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle \frac{8 x^{4}}{4 x^{3}} </code></p>
<p>Simplify. Assume that no denominator equals zero.</p><p><code class='latex inline'>\displaystyle \frac{-75 s^{2} t^{5}}{-25 s^{2} t^{2}} </code></p>
<p>Simplify. Express answers using positive exponents.</p><p><code class='latex inline'>\displaystyle (x^2)^{-3} </code></p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle 3 m^2n \times 4mn^3 </code></p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle (2x^2)^{3 -2m}(\frac{1}{x})^{2m} </code></p>
<p>Simplify. Express each answer with positive exponents.</p><p><code class='latex inline'>\displaystyle x^{4}\left(x^{3}\right) </code></p>
<p>Find each quotient.</p><p><code class='latex inline'>\displaystyle \frac{f^{4} g^{2} h}{x^{2} y} \div f^{3} g </code></p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle \frac{\left(\frac{m^{4}}{m^{5}}\right)}{m^{2}} </code></p>
<p>a. Simplify <code class='latex inline'> a^{n} \cdot a^{-n} </code> .</p><p>b. What is the mathematical relationship between <code class='latex inline'> a^{n} </code> and <code class='latex inline'> a^{-n} ? </code> Explain.</p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle 24 k^5 q^3 \div (2k^q)^2 </code></p>
<p>Simplify and express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle (\frac{(y^2)^6}{y^9})^{-2} </code></p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle (x^{4n -m})(\frac{1}{x^3})^{m + n} </code></p>
<p>Simplify, using the exponent rules. Express each answer in exponential form. </p><p><code class='latex inline'>\displaystyle \left(-6 m^{3}\right)\left(-2 m^{4}\right) </code></p>
<p>Multiply. </p><p><code class='latex inline'>\displaystyle (3 a b)\left(-4 a b^{2}\right) </code></p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle \frac{-45 x^{3} y z^{2}}{-9 x^{2} y} </code></p>
<p>Simplify. Assume that no denominator equals zero.</p><p><code class='latex inline'>\displaystyle \frac{-36 x y^{2}}{4 y^{2}} </code></p>
<p>Simplify and express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{\sqrt{x^2y^4}}{(x^{-2}y^3)^{-1}} </code></p>
<p>Simplify. Express each answer with positive exponents.</p><p><code class='latex inline'>\displaystyle \left(p^{-3}\right)(p)^{5} </code></p>
<p>Simplify.</p><p><code class='latex inline'>y^8\div y^6</code></p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle \frac{20 a^{2} b^{3} c}{-5 a b^{3} c} </code></p>
<p>Simplify.</p><p><code class='latex inline'>(m^4)^3</code></p>
<p><code class='latex inline'>\displaystyle 3^{2 x}=27 </code></p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle [c^{2n -3m}](c^3)^m \div (c^2)^n </code></p>
<p>What is the square-cube law? consider the following sequence of cubes.</p><img src="/qimages/813" /><p> Write a formula to express the area, <code class='latex inline'>A</code>, of one face in terms of the side length, <code class='latex inline'>l</code>.</p>
<p>Simplify.</p><p><code class='latex inline'>\dfrac{2g^2h^3\times (-3g^2h^2)^2}{3gh\times 6g^2h^2}</code></p>
<p>Simplify.</p><p><code class='latex inline'>(2m^3n^2)^4\div (-4mn)^2</code></p>
<p>Error Analysis One student simplified <code class='latex inline'>\displaystyle x^{5}+x^{5} </code> to <code class='latex inline'>\displaystyle x^{10} . </code> A second student simplified <code class='latex inline'>\displaystyle x^{5}+x^{5} </code> to <code class='latex inline'>\displaystyle 2 x^{5} </code>. Which student is correct? Explain.</p>
<p><code class='latex inline'>\displaystyle 3^{-2 x+2}=81 </code></p>
<p>Simplify. Express answers using positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{2x^3 -x^2 + 3x}{x^3} </code></p>
<p>How is the property for raising a quotient to a power similar to the property for raising a product to a power?</p>
<p>Simplify. Express answers using positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{x^5}{x^8} </code></p>
<p>Simplify, using the exponent rules. Express each answer in exponential form. </p><p><code class='latex inline'>\displaystyle y^{4} \times y^{5} </code></p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle \left(x^{2}\right)^{3} </code></p>
<p>Divide. State any restrictions on the variables.</p><p><code class='latex inline'>\displaystyle \frac{7 x}{4 y^{3}} \div \frac{21 x^{3}}{8 y} </code></p>
<p>In 1920, the young nephew of American mathematician Edward Kasner coined the word googo] to mean a really big number. </p><p>1 <code class='latex inline'>\displaystyle googol = 10^{100} </code> then <code class='latex inline'>\displaystyle 1000^{1000} </code> is equivalent to </p><p><strong>A</strong> 1000 googols</p><p><strong>B</strong> 3000 googols</p><p><strong>C</strong> 30 googols</p><p><strong>D</strong> 1000 <code class='latex inline'>googol^{30}</code></p><p><strong>D</strong> 1000 <code class='latex inline'>googol^{googol}</code></p>
<p>Simplify.</p><p><code class='latex inline'>\dfrac{m^{10}}{m^3 \times m^5}</code></p>
<p>Evaluate <code class='latex inline'>\frac{3}{a}\div\frac{a}{3}</code> for each value of <code class='latex inline'>a</code>.</p><p><code class='latex inline'>a=6</code></p>
<p>Simplify and state any restrictions.</p><p><code class='latex inline'>\displaystyle \frac{27p^3q}{18r^2} \div \frac{3p^2q}{36r^4} </code></p>
<p>Are <code class='latex inline'> 3 x^{-2} </code> and <code class='latex inline'> 3 x^{2} </code> reciprocals? Explain.</p>
<p>Simplify. Express each answer with positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{m^{5}}{m^{-3}} </code></p>
<p>a. Open-Ended Write <code class='latex inline'>\displaystyle y^{6} </code> as a product of two powers with the same base in four different ways. Use only positive exponents.</p><p>b. Write <code class='latex inline'>\displaystyle y^{6} </code> as a product of two powers with the same base in four different ways, using negative or zero exponents in each product.</p><p>c. Reasoning How many ways can you write <code class='latex inline'>\displaystyle y^{6} </code> as the product of two powers? Explain your reasoning.</p>
<p>Simplify and state any restrictions.</p><p><code class='latex inline'>\displaystyle \frac{44a^3b}{15b} \div \frac{11a^2}{60b} </code></p>
<p>Simplify.</p><p><code class='latex inline'>8a^5b^3\div 4ab^2</code></p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle n^{x+2} \div n^{x} </code></p>
<p>Multiply. </p><p><code class='latex inline'>\displaystyle \left(8 r^{3} s^{2} t\right)\left(4 s^{3} t\right) </code></p>
<p>Simplify. State any restrictions on the variables. </p><p><code class='latex inline'>\displaystyle \frac{x^2}{2xy}\times \frac{x}{2y^2} \div \frac{(3x)^2}{xy^2}</code></p>
<p>Express each quotient as a product by using negative exponents.</p><p><code class='latex inline'>\displaystyle \frac{x^3 -1}{5x + 2} </code></p>
<p>Multiply. </p><p><code class='latex inline'>\displaystyle (4 x)\left(7 x^{2}\right) </code></p>
<p>Simplify.</p><p><code class='latex inline'>(-c^3)^2\times (-2c)^3</code></p>
<p>Simplify.</p><p><code class='latex inline'>a^5b^4 \times a^3b^2</code></p>
<p>Simplify, using the exponent rules. Express each answer in exponential form. </p><p><code class='latex inline'>\displaystyle \left(-4 a^{3}\right)\left(2 a^{4}\right) </code></p>
<p>Simplify and state any restrictions.</p><p><code class='latex inline'>\displaystyle \frac{16y}{18x} \times \frac{72y}{4x} </code></p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle 5^{x+1} \cdot 5^{1-x} </code></p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle \left(-2 a b^{2}\right)\left(-5 a^{3} b^{3}\right) </code></p>
<p>Simplify. State any restrictions on the variables. <code class='latex inline'> \displaystyle \frac{2x^2}{7} \times \frac{21}{x} </code></p>
<p>Consider the expression <code class='latex inline'>\dfrac{3x^3y\times 6xy^3}{(-3xy)^2}</code></p><p>a) Substitute x = —1 and y = 2 into the expression. Then, evaluate the expression.</p><p>b) Simplify the original expression using the exponent laws. Then, substitute the given values and evaluate the expression.</p><p>c) Describe the advantages and disadvantages of each method.</p>
<p>Simplify. Express answers using positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{c^6}{c^{-3}} </code></p>
<p>Multiply.</p><p><code class='latex inline'>\displaystyle \left(3 x y^{2}\right)\left(-4 x^{3} y^{2}\right) </code></p>
<p>Simplify and state any restrictions.</p><p><code class='latex inline'>\displaystyle \frac{36x^4}{5x^2} \times \frac{80x^3}{12x} </code></p>
<p>Evaluate <code class='latex inline'>\frac{3}{a}\div\frac{a}{3}</code> for each value of <code class='latex inline'>a</code>.</p><p><code class='latex inline'>a=4</code></p>
<p><code class='latex inline'>\displaystyle 2^{y+1}=25 </code></p>
<p>What is the degree of <code class='latex inline'>2u^3v</code>?</p> <ul> <li><strong>A</strong> 1</li> <li><strong>B</strong> 2</li> <li><strong>C</strong> 3</li> <li><strong>D</strong> 4</li> </ul>
<p>Simplify.</p><p><code class='latex inline'>(d^2)^4</code></p>
<p>Express each quotient as a product by using negative exponents.</p><p><code class='latex inline'>\displaystyle \frac{3x^4}{\sqrt{5x + 6}} </code></p>
<p>Simplify and state any restrictions.</p><p><code class='latex inline'>\displaystyle \frac{3x}{32y} \div \frac{27x^2}{96y} </code></p>
<p>Simplify and express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{(n^{-4})n^{-6}}{(n^{-2})^7} </code></p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle d^8 \div d^2 </code></p>
<p>Simplify. Write the expression using only positive exponents. All variables are positive.</p><p><code class='latex inline'>\displaystyle \frac{\sqrt{x^6(y^3)^{-2}}}{(x^3y)^{-2}} </code></p>
<p>Simplify. State any restrictions on the variables.</p><p><code class='latex inline'> \displaystyle \frac{2x}{3} \div \frac{x^2}{5} </code></p>
<p>Multiply. </p><p><code class='latex inline'>\displaystyle \left(-2 x y z^{3}\right)\left(-4 x^{3} y^{2}\right) </code></p>
<p>Simplify.</p><p><code class='latex inline'>\dfrac{3d^4m^3\times 8d^2m^5}{2d^2m^2\times 6d^3m^2}</code></p>
<p>Simplify. Assume that no denominator equals zero.</p><p><code class='latex inline'>\displaystyle \frac{24 x^{4}}{6 x} </code></p>
<p>Daniel said that <code class='latex inline'>\displaystyle \frac{a}{b} \times \frac{c}{d} = \frac{\bigcirc}{\bigcirc} </code>. Complete the</p><p>missing fraction, and explain your thinking.</p>
<p>Simplify. State any restrictions on the variables. </p><p><code class='latex inline'>\displaystyle \frac{5p}{8pq} \div \frac{3p}{12q}</code></p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle \left(\frac{x^{n}}{x^{n-2}}\right)^{3} </code></p>
<p>Simplify and express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{(-2x^5)^3}{8x^{10}} </code></p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle n^2 \times n^3 </code></p>
<p>Simplify and state any restrictions.</p><p><code class='latex inline'>\displaystyle \frac{24b^5}{6b} \times \frac{48b^2}{16b^3} </code></p>
<p>Simplify and express your answers with positive exponents.</p><p><code class='latex inline'>\displaystyle \frac{(x^{-3})x^5}{x^7} </code></p>
<p>a. Use the property for dividing powers with the same base to write <code class='latex inline'> \frac{a^{0}}{a^{n}} </code> as a power of <code class='latex inline'> a </code> .</p><p>b. Use the definition of a zero exponent to simplify <code class='latex inline'> \frac{a^{0}}{a^{n}} </code> .</p><p>C. Reasoning Explain how your results from parts (a) and (b) justify the definition of a negative exponent.</p>
<p>Simplify.</p><p><code class='latex inline'>\displaystyle \frac{-36 m^{3} n^{4} p^{2}}{-9 m^{3} n p} </code></p>
<p>Simplify.</p><p><code class='latex inline'>c^5d^4\div cd</code></p>
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