Answer
$\dfrac{4a^3c^{3}}{5b^{2}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{4a^3b^{-2}}{5c^{-3}} \right)^{1}
$, is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{4a^3b^{-2}}{5c^{-3}}
\\\\=
\dfrac{4a^3c^{3}}{5b^{2}}
.\end{array}