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: 38

Answer

$\color{blue}{\dfrac{9}{p^{11}}}$

Work Step by Step

RECALL: (1) $a^{-m} = \dfrac{1}{a^m}$ (2) $\dfrac{a^m}{a^n} = a^{m-n}$ (3) $\left(\dfrac{a}{b}\right)^m=\dfrac{a^m}{b^m}$ (4) $(ab)^m = a^mb^m$ (5) $(a^m)^n=a^{mn}$ (6) $a^m \cdot a^n = a^{m+n}$ Use rule (4) above to obtain: $=3^2p^{-4(2)} \cdot p^{3(-1)} \\=9p^{-8} \cdot p^{-3}$ Use rule (6) above to obtain: $=9p^{-8+(-3)} \\=9p^{-11}$ Use rule (1) above to obtain: $=9 \cdot \dfrac{1}{p^{11}} \\=\color{blue}{\dfrac{9}{p^{11}}}$
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