Chapter 4 - Section 4.1 - Integer Exponents and Scientific Notation - 4.1 Exercises: 132

$\dfrac{2m^{10}}{9}$

Work Step by Step

Using the laws of exponents, the given expression, $\dfrac{2(-m^{-1})^{-4}}{9(m^{-3})^2} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{2(-1)^{-4}m^{-1(-4)}}{9m^{-3(2)}} \\\\= \dfrac{2(1)m^{4}}{9m^{-6}} \\\\= \dfrac{2m^{4-(-6)}}{9} \\\\= \dfrac{2m^{4+6}}{9} \\\\= \dfrac{2m^{10}}{9} .\end{array}

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