# Chapter 5 - Exponents and Polynomials - 5.6 - Integral Exponents and Scientific Notation - Problem Set 5.6: 83

$\dfrac{x^{4}}{4}$

#### Work Step by Step

Using the laws of exponents, the given expression, $\left( \dfrac{18x^{-1}}{9x^{}} \right)^{-2} ,$ simplifies to \begin{array}{l}\require{cancel} \left( (18\div9)x^{-1-1} \right)^{-2} \\\\= \left( 2x^{-2} \right)^{-2} \\\\= 2^{-2}x^{-2(-2)} \\\\= 2^{-2}x^{4} \\\\= \dfrac{x^{4}}{2^2} \\\\= \dfrac{x^{4}}{4} .\end{array}

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