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

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.3 Multiplying Radical Expressions - 10.3 Exercise Set - Page 647: 49



Work Step by Step

Extracting the factors that are perfect roots of the given index, the given expression, $ \sqrt[3]{x^5y^6z^{10}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[3]{x^3y^6z^{9}\cdot x^2z} \\\\= \sqrt[3]{(xy^2z^{3})^3\cdot x^2z} \\\\= xy^2z^{3}\sqrt[3]{x^2z} \end{array} * Note that it is assumed that no radicands were formed by raising negative numbers to even powers.
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