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: 60

Answer

$(x-2)^3\sqrt[4]{(x-2)^2}$

Work Step by Step

RECALL: $\sqrt[n]{a^n}=a$ Factor the radicand (expression inside the radical sign) so that at least one factor is a perfect fourth power, and then use the rule above to simplify and obtain: $=\sqrt[4]{(x-2)^{12+2}} \\=\sqrt[4]{(x-2)^{12} \cdot (x-2)^2} \\=\sqrt[4]{\left((x-2)^3\right)^4\cdot(x-2)^2} \\=(x-2)^3\sqrt[4]{(x-2)^2}$
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