Answer
$2x$.
Work Step by Step
The given expression is
$=(x^{\frac{2}{3}})(8x)^{\frac{1}{3}}$
Rewrite as cube terms.
$=(x^{\frac{2}{3}})(2^3x)^{\frac{1}{3}}$
Clear the parentheses:
$=x^{\frac{2}{3}}2^{(3\cdot \frac{1}{3})}x^{\frac{1}{3}}$
Simplify.
$=x^{\frac{2}{3}}2x^{\frac{1}{3}}$
Add exponents of powers with the same base.
$=2x^{\frac{2}{3}+\frac{1}{3}}$
Simplify.
$=2x^{\frac{2+1}{3}}$
$=2x^{\frac{3}{3}}$
$=2x$.
