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: 39

Answer

$\color{blue}{\dfrac{p^4}{5}}$

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) $a^m \cdot a^n = a^{m+n}$ (7) $a^0=1, a\ne0$ Use rule (7) above to obtain: $=\dfrac{1}{5p^{-4}}$ Use rule (1) above to obtain: $=\dfrac{1}{5\cdot \frac{1}{p^4}} \\=\dfrac{1}{\frac{5}{p^4}}$ Use the rule $a \div \dfrac{b}{c} = a \cdot \dfrac{c}{b}$ to obtain: $=1 \cdot \dfrac{p^4}{5} \\=\color{blue}{\dfrac{p^4}{5}}$
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