Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Review: 107

Answer

$\dfrac{x^2y^2\sqrt[3]{15yz}}{z}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To rationalize the denominator of the given expression, $ \sqrt[3]{\dfrac{15x^6y^7}{z^2}} ,$ multiply by an expression equal to $1$ which will make the denominator a perfect power of the index. Then extract the root of the factor that is a perfect power of the index. $\bf{\text{Solution Details:}}$ Multiplying the given expression by an expression equal to $1$ which will make the denominator a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[3]{\dfrac{15x^6y^7}{z^2}\cdot\dfrac{z}{z}} \\\\= \sqrt[3]{\dfrac{15x^6y^7z}{z^3}} .\end{array} Extracting the root of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[3]{\dfrac{x^6y^6}{z^3}\cdot15yz} \\\\= \sqrt[3]{\left(\dfrac{x^2y^2}{z}\right)^3\cdot15yz} \\\\= \dfrac{x^2y^2}{z}\sqrt[3]{15yz} \\\\= \dfrac{x^2y^2\sqrt[3]{15yz}}{z} .\end{array}
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