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 7.2 - Rational Exponents - Exercise Set - Page 521: 15



Work Step by Step

RECALL: $a^{\frac{m}{n}}=\sqrt[n]{a^m}$ With $a=-32$, $m=3$, and $n=5$, use the rule above to obtain: $=\sqrt[5]{(-32)^3}$ Write $-32$ as a power of $5$ to obtain: $=\sqrt[5]{[(-2)^5]^3}$ Use the rule $(a^m)^n=a^{mn}$ to obtain: $=\sqrt[5]{(-2)^{5(3)}} \\=\sqrt[5]{(-2)^{15}}$ Use the rule $\sqrt[n]{a^m} = a^{\frac{m}{n}}$ to obtain: $=(-2)^{\frac{15}{5}} \\=(-2)^3 \\=-8$
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