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: 89

Answer

$-12x^3y^4 \sqrt [4]{x^3}$.

Work Step by Step

The given expression is $=(2x^2y\sqrt [4] {8xy})(-3xy^2\sqrt [4]{2x^2y^3})$ Clear the parentheses. $=-6x^3y^3\sqrt [4] {8xy}\sqrt [4] {2x^2y^3}$ Apply the product rule of radicals. $\sqrt [4]a \cdot \sqrt [4] b = \sqrt [4] {ab}$ $=-6x^3y^3\sqrt [4]{8xy\cdot 2x^2y^3}$ Find the square factors. $=-6x^3y^3\sqrt [4]{2^4x^3y^4}$ Factor into two radicals. $=-6x^3y^3\sqrt [4]{2^4y^4}\sqrt [4]{x^3}$ Simplify. $=-6x^3y^3\cdot 2y \sqrt [4]{x^3}$ $=-12x^3y^4 \sqrt [4]{x^3}$.
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