Answer
$\dfrac{a^{20}}{b^{10}c^5}$
Work Step by Step
Using $\left(\dfrac{a}{b}\right)^x=\dfrac{a^x}{b^x}$, then the expression, $
\left(\dfrac{a^4}{b^2c}\right)^5
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(a^4)^5}{(b^2c)^5}
.\end{array}
Using $(a^x)^y=a^{xy}$, then the given expression, $
\dfrac{(a^4)^5}{(b^2c)^5}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{a^{4(5)}}{b^{2(5)}c^5}
\\\\=
\dfrac{a^{20}}{b^{10}c^5}
.\end{array}
