Answer
$\dfrac{2\sqrt[3]{x^2}}{x}$
Work Step by Step
Using $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}},$ the given expression is equivalent to:
\begin{align*}
&
=\dfrac{\sqrt[3]4}{\sqrt[3]{0.5x}}
\end{align*}
Multiplying the numerator and the denominator by an expression equal to $1$ which will make the denominator a perfect power of the index, the expression above is equivalent to
\begin{align*}
&
=\dfrac{\sqrt[3]4}{\sqrt[3]{0.5x}}\cdot\dfrac{\sqrt[3]{0.5^2x^2}}{\sqrt[3]{0.5^2x^2}}
\\\\&=
\dfrac{\sqrt[3]{4(0.25x^2)}}{\sqrt[3]{0.5^3x^3}}
\\\\&=
\dfrac{\sqrt[3]{x^2}}{\sqrt[3]{(0.5x)^3}}
\\\\&=
\dfrac{\sqrt[3]{x^2}}{0.5x}
\\\\&=
\dfrac{\sqrt[3]{x^2}}{\frac{1}{2}x}
\\\\&=
\dfrac{2\sqrt[3]{x^2}}{x}
\end{align*}
Hence, the simplified form of the given expression is $
\dfrac{2\sqrt[3]{x^2}}{x}
$.