Answer
$\dfrac{25t^{6}}{r^{8}}$
Work Step by Step
Using the laws of exponents, the given expression, $
(5r^{-4}t^3)^2
$, is equivalent to
\begin{array}{l}
5^{2}r^{-4(2)}t^{3(2)}
\\\\=
25r^{-8}t^{6}
\\\\=
\dfrac{25t^{6}}{r^{8}}
.\end{array}