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: 58

Answer

$2x^2\sqrt[4]{6x^3}$

Work Step by Step

Write $96$ as $16(6)$ to obtain: $=\sqrt[4]{16(6)x^{11}} \\=\sqrt[4]{2^4(6)x^{11}}$ 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: $=\sqrt[4]{(2^4x^8) \cdot 6x^3} \\=\sqrt[4]{2^4(x^2)^4 \cdot 6x^3} \\=2x^2\sqrt[4]{6x^3}$
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