Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Review: 115

Answer

$\dfrac{xy}{\sqrt[3]{10x^2yz}}$

Work Step by Step

Multiplying both the numerator and the denominator by a factor that will make the numerator a perfect power of the radical, the rationalized-numerator form of the given expression, $ \sqrt[3]{\dfrac{xy^2}{10z}} ,$ is \begin{array}{l}\require{cancel} \sqrt[3]{\dfrac{xy^2}{10z}\cdot\dfrac{x^2y}{x^2y}} \\\\= \sqrt[3]{\dfrac{x^3y^3}{10x^2yz}} \\\\= \sqrt[3]{\dfrac{(xy)^3}{10x^2yz}} \\\\= \dfrac{xy}{\sqrt[3]{10x^2yz}} .\end{array}
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