Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.2 - Rational Exponents - 7.2 Exercises: 30

Answer

9

Work Step by Step

As shown on page 445, we know that $a^{\frac{m}{n}}=\sqrt[n] a^{m}=(\sqrt[n] a)^{m}$. Therefore, $(-243)^{\frac{2}{5}}=\sqrt[5] (-243)^{2}=(\sqrt[5] -243)^{2}=(-3)^{2}=9$. We know that $\sqrt[5] -243=-3$, because $(-3)^{5}=-243$.
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