Answer
$3x\sqrt[3] {2x^2}$.
Work Step by Step
The given expression is
$=\sqrt[3] {54x^5}$
Rewrite as an exponential expression.
$\Rightarrow =(54x^5)^{\frac{1}{3}}$
Factor the terms:
$\Rightarrow =(3^3\cdot 2x^3\cdot x^2)^{\frac{1}{3}}$
Raise each factor in parentheses to the $\frac{1}{3}$ power.
$\Rightarrow 2x=(2^{\frac{1}{3}}x^{\frac{1}{3}})\cdot g(x)$
The given expression is
$=\sqrt[3] {54x^5}$
Factor the radicands:
$=\sqrt[3] {3^3\cdot 2x^3\cdot x^2}$
Group the perfect cube factors.
$=\sqrt[3] {3^3x^3\cdot 2\cdot x^2}$
Factor into two radicals.
$=\sqrt[3] {3^3x^3}\cdot \sqrt[3] {2\cdot x^2}$
Simplify.
$=3x\sqrt[3] {2x^2}$.
