## 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: 55

#### Answer

$-2a^{4}\sqrt[3]{10a^2}$

#### Work Step by Step

Extracting the factors that are perfect roots of the given index, the given expression, $\sqrt[3]{-80a^{14}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[3]{-8a^{12}\cdot 10a^2} \\\\= \sqrt[3]{(-2a^{4})^3\cdot 10a^2} \\\\= -2a^{4}\sqrt[3]{10a^2} \end{array} * Note that it is assumed that no radicands were formed by raising negative numbers to even powers.

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