## 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: 22

#### Answer

$\dfrac{3x}{y^2z}$

#### Work Step by Step

Using the properties of radicals, the given expression, $\sqrt[4]{\dfrac{81x^4}{y^8z^4}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt[4]{81x^4}}{\sqrt[4]{y^8z^4}} \\\\= \dfrac{\sqrt[4]{(3x)^4}}{\sqrt[4]{(y^2z)^4}} \\\\= \dfrac{3x}{y^2z} \end{array} * Note that it is assumed that all variables represent positive numbers.

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