Answer
$\dfrac{27a^{9}}{64z^{15}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{5z^3}{2a^2} \right)^{-3} \left( \dfrac{8a^{-1}}{15z^{-2}} \right)^{-3}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\left( \dfrac{2a^2}{5z^3} \right)^{3} \left( \dfrac{15z^{-2}}{8a^{-1}} \right)^{3}
\\\\=
\dfrac{2^3a^{2(3)}}{5^3z^{3(3)}}\cdot \dfrac{15^3z^{-2(3)}}{8^3a^{-1(3)}}
\\\\=
\dfrac{2^3a^{6}}{5^3z^{9}}\cdot \dfrac{15^3z^{-6}}{8^3a^{-3}}
\\\\=
\dfrac{2^3\cdot15^3a^{6}z^{-6}}{5^3\cdot8^3z^{9}a^{-3}}
\\\\=
\dfrac{2^3\cdot3^3\cdot\cancel{5^3}a^{6}z^{-6}}{\cancel{5^3}\cdot2^9z^{9}a^{-3}}
\\\\=
2^{3-9}\cdot3^3\cdot a^{6-(-3)}z^{-6-9}
\\\\=
2^{-6}\cdot27\cdot a^{9}z^{-15}
\\\\=
\dfrac{27a^{9}}{2^{6}z^{15}}
\\\\=
\dfrac{27a^{9}}{64z^{15}}
.\end{array}