Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - Test: Chapter 10: 18

Answer

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

Work Step by Step

Multiplying by an expression equal to $1$ which will make the denominator a perfect power of the index, the given expression is equivalent to\begin{array}{l}\require{cancel} \dfrac{\sqrt[3]{x}}{\sqrt[3]{4y}} \\\\= \dfrac{\sqrt[3]{x}}{\sqrt[3]{4y}}\cdot\dfrac{\sqrt[3]{2y^2}}{\sqrt[3]{2y^2}} \\\\= \dfrac{\sqrt[3]{x(2y^2)}}{\sqrt[3]{4y(2y^2)}} \\\\= \dfrac{\sqrt[3]{2xy^2}}{\sqrt[3]{8y^3}} \\\\= \dfrac{\sqrt[3]{2xy^2}}{\sqrt[3]{(2y)^3}} \\\\= \dfrac{\sqrt[3]{2xy^2}}{2y} .\end{array}
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