Answer
$\dfrac{1}{5z^{9}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{(-z^{-2})^3}{5(z^{-3})^{-1}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(-z)^{-2(3)}}{5z^{-3(-1)}}
\\\\=
\dfrac{(-z)^{-6}}{5z^{3}}
\\\\=
\dfrac{1}{5z^{3}(-z)^{6}}
\\\\=
\dfrac{1}{5z^{3}z^{6}}
\\\\=
\dfrac{1}{5z^{3+6}}
\\\\=
\dfrac{1}{5z^{9}}
.\end{array}
