Answer
$\dfrac{b^{5/6}}{49a^{1/4}c^{5/3}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{49c^{5/3}}{a^{-1/4}b^{5/6}} \right)^{-1}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{1}{\left( \dfrac{49c^{5/3}}{a^{-1/4}b^{5/6}} \right)^{1}}
\\\\=
\dfrac{a^{-1/4}b^{5/6}}{49c^{5/3}}
\\\\=
\dfrac{b^{5/6}}{49a^{1/4}c^{5/3}}
.\end{array}
