Answer
$-4+4\sqrt{3}$.
Work Step by Step
The given expression is
$=\frac{8}{1+\sqrt{3}}$
The conjugate of $1+\sqrt{3}$ is $1-\sqrt{3}$.
Multiply by $\frac{\sqrt[3]{2}}{\sqrt[3]{2}}$.
$=\frac{8}{1+\sqrt{3}}\cdot \frac{1-\sqrt{3}}{1-\sqrt{3}}$
Use sum and difference pattern.
$=\frac{8(1-\sqrt{3})}{1^2-(\sqrt{3})^2}$
Simplify.
$=\frac{8(1-\sqrt{3})}{1-3}$
$=\frac{8(1-\sqrt{3})}{-2}$
$=-4(1-\sqrt{3})$
Use distributive property.
$=-4+4\sqrt{3}$.
