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: 84

Answer

$x^3y^{10}z^2 \sqrt[3] {4xz} $.

Work Step by Step

The given expression is $=\frac{-x^2y^7}{2}\left ( \sqrt[3] {-32x^4y^9z^7} \right )$ Identify perfect cube factors. $=\frac{-x^2y^7}{2}\left ( \sqrt[3] {(-1)^32^32^2x^3x^1y^3y^3y^3z^3z^3z^1} \right )$ Factor into two radicals. $=\frac{-x^2y^7}{2}\left ( \sqrt[3] {(-1)^32^3x^3y^3y^3y^3z^3z^3}\sqrt[3] {2^2x^1z^1} \right )$ $=\frac{-x^2y^7}{2}\cdot (-1)2xyyyzz\left ( \sqrt[3] {4xz} \right )$ Simplify. $=x^3y^{10}z^2\left ( \sqrt[3] {4xz} \right )$.
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