## Elementary Algebra

Published by Cengage Learning

# Chapter 9 - Roots and Radicals - 9.2 - Simplifying Radicals - Problem Set 9.2 - Page 406: 52

#### Answer

$-4a^{5}$

#### Work Step by Step

Using the properties of radicals, the given expression, $-\dfrac{2}{7}\sqrt[]{196a^{10}} ,$ simplifies to \begin{array}{l}\require{cancel} -\dfrac{2}{7}\sqrt[]{(14a^{5})^2} \\\\= -\dfrac{2}{7}\cdot14a^{5} \\\\= -\dfrac{2}{\cancel{7}}\cdot\cancel{7}\cdot2a^{5} \\\\= -4a^{5} .\end{array} Note that all of the variables are assumed to represent non-negative real numbers.

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