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

Published by Pearson

# Chapter 10 - Exponents and Radicals - 10.3 Multiplying Radical Expressions - 10.3 Exercise Set - Page 647: 76

#### Answer

$a^{2}(b-c)^{}\sqrt[5]{(b-c)^3}$

#### Work Step by Step

Using the properties of radicals, the given expression, $\sqrt[5]{a^3(b-c)^4}\sqrt[5]{a^7(b-c)^4} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[5]{a^3(b-c)^4\cdot a^7(b-c)^4} \\\\= \sqrt[5]{a^{3+7}(b-c)^{4+4}} \\\\= \sqrt[5]{a^{10}(b-c)^{8}} \\\\= \sqrt[5]{a^{10}(b-c)^{5}\cdot(b-c)^3} \\\\= \sqrt[5]{\left[ a^{2}(b-c)^{} \right]^5\cdot(b-c)^3} \\\\= a^{2}(b-c)^{}\sqrt[5]{(b-c)^3} \end{array} * Note that it is assumed that no radicands were formed by raising negative numbers to even powers.

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