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