Answer
$\sqrt[6]{\dfrac{243c^5}{32a^5b^5}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{2ab}{3c} \right)^{-5/6}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\left( \dfrac{3c}{2ab} \right)^{5/6}
.\end{array}
Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $
\left( \dfrac{3c}{2ab} \right)^{5/6}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[6]{\left( \dfrac{3c}{2ab} \right)^{5}}
\\\\=
\sqrt[6]{\dfrac{3^5c^5}{2^5a^5b^5}}
\\\\=
\sqrt[6]{\dfrac{243c^5}{32a^5b^5}}
.\end{array}
