Answer
$\dfrac{1}{8x^3}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{2x^{-1}}{x^{-2}} \right)^{-3}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2^{-3}x^{-1(-3)}}{x^{-2(-3)}}
\\\\=
\dfrac{2^{-3}x^{3}}{x^{6}}
\\\\=
2^{-3}x^{3-6}
\\\\=
2^{-3}x^{-3}
\\\\=
\dfrac{1}{2^{3}x^3}
\\\\=
\dfrac{1}{8x^3}
.\end{array}
