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

Published by Pearson

# Chapter 10 - Exponents and Radicals - 10.4 Dividing Radical Expressions - 10.4 Exercise Set - Page 653: 39

#### Answer

$2x^{2}y^{3}\sqrt[4]{y^3}$

#### Work Step by Step

Using the properties of radicals, the given expression, $\dfrac{\sqrt[4]{48x^9y^{13}}}{\sqrt[4]{3xy^{-2}}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[4]{\dfrac{48x^9y^{13}}{3xy^{-2}}} \\\\= \sqrt[4]{16x^{9-1}y^{13-(-2)}} \\\\= \sqrt[4]{16x^{8}y^{15}} \\\\= \sqrt[4]{16x^{8}y^{12}\cdot y^3} \\\\= \sqrt[4]{(2x^{2}y^{3})^4\cdot y^3} \\\\= 2x^{2}y^{3}\sqrt[4]{y^3} .\end{array} * Note that it is assumed that all variables represent positive numbers.

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