Answer
$2x\sqrt[3] { x }$.
Work Step by Step
The given expression is
$\frac{\sqrt[3] {16x^8}}{\sqrt[3] {2x^4}}$
Use quotient rule.
$\sqrt[3] {\frac{ {16x^8}}{2x^4}}$
Factor the given expression:
$=\sqrt[3] {\frac{{2^3\cdot 2\cdot x^3\cdot x^3\cdot x^2}}{{2x^3\cdot x}}}$
Simplify.
$=\sqrt[3] {2^3\cdot x^3\cdot x }$
$=2\cdot x\sqrt[3] { x }$
$=2x\sqrt[3] { x }$.
