Answer
$\dfrac{a^{4}b^{8}}{c^{12}}$
Work Step by Step
In order to simplify the expression, we distribute the 4 into the parenthesis. Thus, using the laws of exponents, the given expression, $
\left( \dfrac{ab^2}{c^3} \right)^{4}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{a^{1(4)}b^{2(4)}}{c^{3(4)}}
\\\\=
\dfrac{a^{4}b^{8}}{c^{12}}
.\end{array}