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: 57

Answer

$2x^2\sqrt[4]{5x^2}$

Work Step by Step

Write $80$ as $16(5)$ to obtain: $=\sqrt[4]{16(5)x^{10}} \\=\sqrt[4]{2^4(5)x^{10}}$ 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: $=\sqrt[4]{(2^4x^8) \cdot 5x^2} \\=\sqrt[4]{2^4(x^2)^4 \cdot 5x^2} \\=2x^2\sqrt[4]{5x^2}$
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