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: 81

Answer

$(x-y)^2\sqrt[3] {(x-y)^{2}}$.

Work Step by Step

The given expression is $=\sqrt[3] {x-y} \cdot \sqrt[3] {(x-y)^7}$ Apply product rule $=\sqrt[n] a \cdot \sqrt[n] b = \sqrt[n] {ab}$ $=\sqrt[3] {(x-y) \cdot (x-y)^7}$ $=\sqrt[3] {(x-y)^1 \cdot (x-y)^7}$ Use $a^n\cdot a^m = a^{m+n}$ $=\sqrt[3] {(x-y)^{1+7}}$ $=\sqrt[3] {(x-y)^{8}}$ Further simplify by using product rule. $=\sqrt[3] {(x-y)^{3+3+2}}$ $=\sqrt[3] {(x-y)^{3}(x-y)^{3}(x-y)^{2}}$ $=(x-y)(x-y)\sqrt[3] {(x-y)^{2}}$ $=(x-y)^2\sqrt[3] {(x-y)^{2}}$.
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