Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.3 - Multiplying and Simplifying Radical Expressions - Exercise Set - Page 531: 83

Answer

$-6x^3y^3 \sqrt[3] {2yz^2} $.

Work Step by Step

The given expression is $=-2x^2y\left ( \sqrt[3] {54x^3y^7z^2} \right )$ Identify perfect cube factors. $=-2x^2y\left ( \sqrt[3] {3^3\cdot2x^3y^3y^3yz^2} \right )$ Factor into two radicals. $=-2x^2y\left ( \sqrt[3] {3^3x^3y^3y^3}\sqrt[3] {2yz^2} \right )$ $=-2x^2y\cdot 3xyy\left ( \sqrt[3] {2yz^2} \right )$ Simplify. $=-6x^3y^3\left ( \sqrt[3] {2yz^2} \right )$.
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