Answer
$5$
Work Step by Step
The given expression, $
\dfrac{125^{-4}(25^2)^4}{125}
$, simplifies to
\begin{array}{l}
\dfrac{125^{-4}25^{8}}{125}
\\\\=
\dfrac{(5^3)^{-4}(5^2)^{8}}{5^3}
\\\\=
\dfrac{5^{-12}5^{16}}{5^3}
\\\\=
5^{-12+16-3}
\\\\=
5^{1}
\\\\=
5
.\end{array}