Intermediate Algebra (6th Edition)

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

Chapter 7 - Review: 70

Answer

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

Work Step by Step

Using the properties of radicals, the given expression, $ \sqrt[3]{\dfrac{y^5}{27x^6}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[3]{\dfrac{y^3}{27x^6}\cdot y^2} \\\\= \sqrt[3]{\left( \dfrac{y}{3x^2} \right)^3\cdot y^2} \\\\= \dfrac{y}{3x^2}\sqrt[3]{y^2} \\\\= \dfrac{y\sqrt[3]{y^2}}{3x^2} .\end{array}
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