Answer
The required value is $2x\sqrt[3]{2x}$
Work Step by Step
Consider the expression,
$\sqrt[3]{16{{x}^{4}}}$
The given expression can be further evaluated as
$\begin{align}
& \sqrt[3]{16{{x}^{4}}}=\sqrt[3]{\left( 8 \right)\left( 2 \right)\left( {{x}^{3}} \right)\left( x \right)} \\
& =\sqrt[3]{8}\sqrt[3]{{{x}^{3}}}\sqrt[3]{2x} \\
& =\sqrt[3]{{{\left( 2 \right)}^{2}}}\sqrt[3]{{{\left( x \right)}^{3}}}\sqrt[3]{2x} \\
& =2x\sqrt[3]{2x}
\end{align}$
Therefore, the value of $\sqrt[3]{16{{x}^{4}}}$ is $2x\sqrt[3]{2x}$.
