Answer
$\dfrac{2\sqrt[4]{9x}}{3x^2}$
Work Step by Step
Rationalizing the denominator of $
\sqrt[4]{\dfrac{16}{9x^7}}
$ results to
\begin{array}{l}
\sqrt[4]{\dfrac{16}{9x^7}}
\cdot
\sqrt[4]{\dfrac{9x}{9x}}
\\\\=
\sqrt[4]{\dfrac{16\cdot9x}{81x^8}}
\\\\=
\dfrac{2\sqrt[4]{9x}}{3x^2}
.\end{array}