Answer
$\dfrac{x^{2}}{9}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( 3x^{-1} \right)^{-2}
,$ simplifies to
\begin{array}{l}\require{cancel}
3^{1(-2)}x^{-1(-2)}
\\\\=
3^{-2}x^{2}
\\\\=
\dfrac{x^{2}}{3^{2}}
\\\\=
\dfrac{x^{2}}{9}
.\end{array}