Answer
$\dfrac{1}{16y^{18}}$
Work Step by Step
Using the laws of exponents and the Distributive Property, the given expression, $
(y^6)^{-5}(2y^{-3})^{-4}
,$ simplifies to
\begin{array}{l}\require{cancel}
y^{6(-5)}(2^{-4}y^{-3(-4)})
\\\\=
y^{-30}(2^{-4}y^{12})
\\\\=
2^{-4}y^{-30+12}
\\\\=
2^{-4}y^{-18}
\\\\=
\dfrac{1}{2^{4}y^{18}}
\\\\=
\dfrac{1}{16y^{18}}
.\end{array}