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}
