# Chapter 4 - Section 4.1 - Integer Exponents and Scientific Notation - 4.1 Exercises: 141

$\dfrac{n^{10}}{25m^{18}}$

#### Work Step by Step

Using the laws of exponents, the given expression, $\left( \dfrac{5m^4n^{-3}}{m^{-5}n^2} \right)^{-2} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{5^{-2}m^{4(-2)}n^{-3(-2)}}{m^{-5(-2)}n^{2(-2)}} \\\\= \dfrac{5^{-2}m^{-8}n^{6}}{m^{10}n^{-4}} \\\\= 5^{-2}m^{-8-10}n^{6-(-4)} \\\\= 5^{-2}m^{-8-10}n^{6+4} \\\\= 5^{-2}m^{-18}n^{10} \\\\= \dfrac{n^{10}}{5^{2}m^{18}} \\\\= \dfrac{n^{10}}{25m^{18}} .\end{array}

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