# Chapter 10 - Exponents and Radicals - 10.4 Dividing Radical Expressions - 10.4 Exercise Set - Page 653: 57

$\dfrac{\sqrt[5]{9y^4}}{2xy}$

#### Work Step by Step

Rationalizing the denominator of the given expression, $\sqrt[5]{\dfrac{9}{32x^5y}} ,$ we find: \begin{array}{l}\require{cancel} \sqrt[5]{\dfrac{9}{32x^5y}\cdot\dfrac{y^4}{y^4}} \\\\= \sqrt[5]{\dfrac{9y^4}{32x^5y^5}} \\\\= \dfrac{\sqrt[5]{9y^4}}{\sqrt[5]{32x^5y^5}} \\\\= \dfrac{\sqrt[5]{9y^4}}{\sqrt[5]{(2xy)^5}} \\\\= \dfrac{\sqrt[5]{9y^4}}{2xy} .\end{array} * Note that it is assumed that all variables represent positive numbers.

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