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: 18



Work Step by Step

Simplify the radicand (expression inside the radicla sign) to obtain: $$ \sqrt[3]{\frac{3xy^2}{81x^4y^2}}=\sqrt[3]{\frac{1}{27x^3}}==\sqrt[3]{\frac{1}{(3x)^3}}$$ Use the rule $\sqrt[n]{a^n}=a, a\gt0$ to obtain $$\sqrt[3]{\frac{1}{(3x)^3}}=\frac{1}{3x} $$
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