Answer
$-16x^{11}y^{17}$
Work Step by Step
Using the laws of exponents, the given expression, $
(-2x^2y^2)^4(-xy^3)^3
,$ simplifies to
\begin{array}{l}\require{cancel}
(-2)^{1(4)}x^{2(4)}y^{2(4)}\cdot(-1)^3x^{1(3)}y^{3(3)}
\\\\=
(-2)^{4}x^{8}y^{8}\cdot(-1)^3x^{3}y^{9}
\\\\=
16x^{8}y^{8}\cdot(-1)x^{3}y^{9}
\\\\=
16(-1)x^{8+3}y^{8+9}
\\\\=
-16x^{11}y^{17}
.\end{array}