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