Answer
$\dfrac{3\sqrt[4]{2}}{2}$
Work Step by Step
Rationalizing the denominator of $
\sqrt[4]{\dfrac{81}{8}}
$ results to
\begin{array}{l}
\sqrt[4]{\dfrac{81}{8}}
\cdot
\sqrt[4]{\dfrac{2}{2}}
\\\\=
\sqrt[4]{\dfrac{81\cdot2}{16}}
\\\\=
\dfrac{3\sqrt[4]{2}}{2}
.\end{array}