## 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: 75

#### Answer

$x^{}(y+z)^{2}\sqrt[5]{x}$

#### Work Step by Step

Using the properties of radicals, the given expression, $\sqrt[5]{x^3(y+z)^6}\sqrt[5]{x^3(y+z)^4} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[5]{x^3(y+z)^6\cdot x^3(y+z)^4 } \\\\= \sqrt[5]{x^{3+3}(y+z)^{6+4}} \\\\= \sqrt[5]{x^{6}(y+z)^{10}} \\\\= \sqrt[5]{x^{5}(y+z)^{10}\cdot x} \\\\= \sqrt[5]{\left[ x^{}(y+z)^{2} \right]^5\cdot x} \\\\= x^{}(y+z)^{2}\sqrt[5]{x} \end{array} * Note that it is assumed that no radicands were formed by raising negative numbers to even powers.

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