Answer
$-\dfrac{y^{3}}{27}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( -3y^{-1} \right)^{-3}
,$ simplifies to
\begin{array}{l}\require{cancel}
(-3)^{1(-3)}y^{-1(-3)}
\\\\=
(-3)^{-3}y^{3}
\\\\=
\dfrac{y^{3}}{(-3)^{3}}
\\\\=
\dfrac{y^{3}}{-27}
\\\\=
-\dfrac{y^{3}}{27}
.\end{array}