#### Answer

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

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\sqrt[4]{\dfrac{16}{x}}
,$ multiply the numerator and the denominator by an expression equal to $1$ which will make the denominator a perfect power of the index.
$\bf{\text{Solution Details:}}$
Multiplying the numerator and the denominator by an expression equal to $1$ which will make the denominator a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt[4]{\dfrac{16}{x}\cdot\dfrac{x^3}{x^3}}
\\\\=
\sqrt[4]{\dfrac{16x^3}{x^4}}
.\end{array}
Rewriting the radicand using an expression that contains a factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt[4]{\dfrac{16}{x^4}\cdot x^3}
\\\\=
\sqrt[4]{\left( \dfrac{2}{x} \right)^4\cdot x^3}
.\end{array}
Extracting the root of the radicand that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\dfrac{2}{x}\sqrt[4]{ x^3}
\\\\=
\dfrac{2\sqrt[4]{ x^3}}{x}
.\end{array}