#### Answer

$x=\{ 0,8 \}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
x^{2/3}=2x^{1/3}
,$ raise both sides to the third power to get rid of the denominator in the fractional exponent. Then express the resulting equation in the form $ax^2+bx+c=0,$ and use the concepts of factoring quadratic equations to solve the resulting equation. Finally, do checking if the solution satisfies the original equation.
$\bf{\text{Solution Details:}}$
Raising both sides to the third power, the given equation becomes
\begin{array}{l}\require{cancel}
\left(x^{2/3}\right)^3=\left( 2x^{1/3} \right)^3
.\end{array}
Using the extended Power Rule of the laws of exponents which is given by $\left( x^my^n \right)^p=x^{mp}y^{np},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
x^{\frac{2}{3}\cdot3 }=2^3x^{\frac{1}{3}\cdot3}
\\\\
x^2=8x
\\\\
x^2-8x=0
.\end{array}
Factoring the $GCF=x,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
x(x-8)=0
.\end{array}
Equating each factor to zero (Zero Product Property), then
\begin{array}{l}\require{cancel}
x=0
\\\\\text{OR}\\\\
x-8=0
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
x=0
\\\\\text{OR}\\\\
x-8=0
\\\\
x=8
.\end{array}
Upon checking, $
x=\{ 0,8 \}
$ satisfies the original equation.