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: 16

Answer

$9$

Work Step by Step

RECALL: $a^{\frac{m}{n}}=\sqrt[n]{a^m}$ With $a=-27$, $m=2$, and $n=3$, use the rule above to obtain: $=\sqrt[3]{(-27)^2}$ Write $-27$ as a power of $3$ to obtain: $=\sqrt[3]{[(-3)^3]^2}$ Use the rule $(a^m)^n=a^{mn}$ to obtain: $=\sqrt[3]{[(-3)^3]^2} \\=\sqrt[3]{(-3)^6} $ Use the rule $\sqrt[n]{a^m} = a^{\frac{m}{n}}$ to obtain: $=(-3)^{\frac{6}{3}} \\=(-3)^2 \\=9$
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