$\begin{align}  & {{\left( \sqrt[3]{64{{a}^{3}}} \right)}^{-1}}={{\left( \sqrt[3]{{{4}^{3}}{{a}^{3}}} \right)}^{-1}} \\ & ={{\left[ {{\left( 4a \right)}^{3}} \right]}^{-\tfrac{1}{3}}}={{(4a)}^{-1}}=\frac{1}{4a} \\ & \text{or} \\ & {{\left( \sqrt[3]{64{{a}^{3}}} \right)}^{-1}}=\frac{1}{\left( \sqrt[3]{{{4}^{3}}{{a}^{3}}} \right)}=\frac{1}{{{4}^{\tfrac{3}{3}}}{{a}^{\tfrac{3}{3}}}}=\frac{1}{4a} \end{align}$