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: 56

Answer

$2xy^3\sqrt[5]{2x^2y}$

Work Step by Step

Write $64$ as $2^6$ to obtain: $=\sqrt[5]{2^6x^7y^{16}}$ RECALL: $\sqrt[n]{a^n}=a$ Factor the radicand (expression inside the radical sign) so that at least one factor is a perfect fifth power, and then use the rule above to simplify and obtain: $=\sqrt[5]{(2^5x^5y^{15}) \cdot 2x^2y} \\=\sqrt[5]{2^5x^5(y^3)^5 \cdot 2x^2y} \\=2xy^3\sqrt[5]{2x^2y}$
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