Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Appendix A - Review - A.7 nth Roots; Rational Exponents - A.7 Assess Your Understanding - Page A60: 14

Answer

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

Work Step by Step

Factor the radicand (expression inside the radical sign) so that some factors are perfect roots (4th power) to obtain: $$=\sqrt[4]{(16x^4)(3x)}\\ =\sqrt[4]{(2x)^4(3x)}$$ Use the Product Rule $\sqrt[n]{ab}=\sqrt[n]{a}\cdot \sqrt[n]{b}\quad$ and $\quad \sqrt[n]{a^n}=n, a\ge0$, to obtain $$ =\sqrt[4]{(2x)^4} \cdot \sqrt[4]{3x}\\ =2x\sqrt[4]{3x} $$
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