Answer
$25x^{7}y^{8}$
Work Step by Step
Using the laws of exponents, the given expression, $
(5x^2y)^2(xy^2)^3
,$ simplifies to
\begin{array}{l}\require{cancel}
\left( 5^{1(2)}x^{2(2)}y^{1(2)} \right)\left( x^{1(3)}y^{2(3)}\right)
\\\\=
\left( 5^{2}x^{4}y^{2} \right)\left( x^{3}y^{6}\right)
\\\\=
\left( 25x^{4}y^{2} \right)\left( x^{3}y^{6}\right)
\\\\=
25x^{4+3}y^{2+6}
\\\\=
25x^{7}y^{8}
.\end{array}
