College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.6 - Rational Exponents - R.6 Exercises: 31

Answer

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

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the laws of exponents to simplify the given expression, $ \dfrac{(p^{-2})^0}{5p^{-4}} .$ $\bf{\text{Solution Details:}}$ Since any expression (except 0) raised to the power of zero is $1$, the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{1}{5p^{-4}} .\end{array} Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{p^{4}}{5} .\end{array}
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