## College Algebra (11th Edition)

Published by Pearson

# Chapter R - Section R.6 - Rational Exponents - R.6 Exercises - Page 56: 32

#### Answer

$\dfrac{m^{3}}{9}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the laws of exponents to simplify the given expression, $\dfrac{(m^4)^0}{9m^{-3}} .$ $\bf{\text{Solution Details:}}$ 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}{9m^{-3}} .\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{m^{3}}{9} .\end{array}

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