## Elementary Algebra

Published by Cengage Learning

# Chapter 9 - Roots and Radicals - 9.2 - Simplifying Radicals - Problem Set 9.2 - Page 406: 49

#### Answer

$\dfrac{5x\sqrt[3]{2x}}{8}$

#### Work Step by Step

Using the properties of radicals, the given expression, $\dfrac{1}{8}\sqrt[3]{250x^4} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{1}{8}\sqrt[3]{125x^3\cdot2x} \\\\= \dfrac{1}{8}\sqrt[3]{(5x)^3\cdot2x} \\\\= \dfrac{1}{8}\cdot5x\sqrt[3]{2x} \\\\= \dfrac{5x}{8}\sqrt[3]{2x} \\\\= \dfrac{5x\sqrt[3]{2x}}{8} .\end{array} Note that all of the variables are assumed to represent non-negative real numbers.

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