Answer
$\dfrac{y^{4}}{36}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{6^{-1}y^3(y^2)^{-2}}{6y^{-4}(y^{-1})}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{y^3(y^{2(-2)})}{6(6^{1})y^{-4}(y^{-1})}
\\\\=
\dfrac{y^3(y^{-4})}{36y^{-4}(y^{-1})}
\\\\=
\dfrac{y^{3+(-4)-(-4)-(-1)}}{36}
\\\\=
\dfrac{y^{3-4+4+1}}{36}
\\\\=
\dfrac{y^{4}}{36}
.\end{array}