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