#### Answer

$9p^4-6p^2q^3+q^6$

#### Work Step by Step

Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the given expression, $
(3p^2-q^3)^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
(3p^2)^2+2(3p^2)(-q^3)+(-q^3)^2
\\\\=
9p^4-6p^2q^3+q^6
.\end{array}