Answer
$\frac{7\sqrt[3]{4x}}{ x}$.
Work Step by Step
The given expression is
$=\frac{14}{\sqrt[3]{2x^2}}$
Multiply the numerator and the denominator by $\sqrt[3]{(2x^2)^2}$.
$=\frac{14}{\sqrt[3]{2x^2}}\cdot \frac{\sqrt[3]{(2x^2)^2}}{\sqrt[3]{(2x^2)^2}}$
Use product rule.
$=\frac{14\sqrt[3]{(2x^2)^2}}{\sqrt[3]{(2x^2)\cdot (2x^2)^2}}$
Simplify.
$=\frac{14\sqrt[3]{(2x^2)^2}}{\sqrt[3]{ (2x^2)^{2+1}}}$
$=\frac{14\sqrt[3]{(2x^2)^2}}{\sqrt[3]{ (2x^2)^{3}}}$
$=\frac{14\sqrt[3]{4x^4}}{ 2x^2}$
Factor the radicands.
$=\frac{14\sqrt[3]{4x^3x}}{ 2x^2}$
Simplify.
$=\frac{14\sqrt[3]{4x}x}{ 2x^2}$
Cancel common terms.
$=\frac{7\sqrt[3]{4x}}{ x}$.
