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: 88

Answer

$\color{blue}{p-\dfrac{1}{p}}$

Work Step by Step

RECALL: $(a-b)(a+b)=a^2-b^2$ Use the formula above with $a=p^{1/2}$ and $b=p^{-1/2}$ to obtain : $=(p^{1/2})^2 - (p^{-1/2})^2$ Use the rule $(a^m)^n=a^{mn}$ to obtain: $=p^{(1/2)(2)} - p^{(-1/2)(2)} \\=p^1 - p^{-1}$ Use the rule $a^{-m} = \dfrac{1}{a^m}$ to obtain: $=p-\dfrac{1}{p^1} \\=\color{blue}{p-\dfrac{1}{p}}$
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