Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.6 Rational Exponents - R.6 Exercises - Page 62: 2



Work Step by Step

RECALL: (1) $a^{-m} = \dfrac{1}{a^m}$ (2) $\left(\dfrac{a}{b}\right)^m = \dfrac{a^m}{b^m}$ Use the rule (1) above to obtain: $(\frac{2}{3})^{-2} = \dfrac{1}{(\frac{2}{3})^2}$ Use rule (2) above to obtain: $=\dfrac{1}{(\frac{2^2}{3^2})}$ Use the rule $a \div \frac{b}{c}=a \cdot \frac{c}{b}$ to obtain: $=1 \cdot \left(\frac{3^2}{2^2}\right) \\=\dfrac{3^2}{2^2}$ Use rule (2) above to obtain: $=\left(\dfrac{3}{2}\right)^2$ Thus, the given statement is true.
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