Answer
$\dfrac{1}{y^{11}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{y^{-3}}{(y^4)^2}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{y^{-3}}{y^{4(2)}}
\\\\=
\dfrac{y^{-3}}{y^{8}}
\\\\=
y^{-3-8}
\\\\=
y^{-11}
\\\\=
\dfrac{1}{y^{11}}
.\end{array}