#### Answer

$\dfrac{2a^{2}\sqrt[4]{3a^3}}{c^2}$

#### Work Step by Step

Extracting the factors that are perfect powers of the index, the given expression simplifies to
\begin{array}{l}\require{cancel}
\sqrt[4]{\dfrac{48a^{11}}{c^8}}
\\\\=
\sqrt[4]{\dfrac{16a^{8}}{c^8}\cdot3a^3}
\\\\=
\sqrt[4]{\left( \dfrac{2a^{2}}{c^2}\right)^4\cdot3a^3}
\\\\=
\dfrac{2a^{2}}{c^2}\sqrt[4]{3a^3}
\\\\=
\dfrac{2a^{2}\sqrt[4]{3a^3}}{c^2}
.\end{array}
Note that all variables are assumed to represent positive numbers.