#### Answer

$x=\{-8,8\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $ x^{2/3}=4 ,$ raise both sides to the third power to cancel the denominator of the exponent. Then take the square root of both sides and simplify the resulting radical.
$\bf{\text{Solution Details:}}$
Raising both sides of the equation to the third power, the equation above is equivalent to
\begin{array}{l}\require{cancel}
\left( x^{\frac{2}{3}} \right)^{3}=(4)^{3}
\\\\
x^2=64
.\end{array}
Taking the square root of both sides and simplifying the radical, the solutions are
\begin{array}{l}\require{cancel}
x=\pm\sqrt{64}
\\\\
x=\pm\sqrt{(8)^2}
\\\\
x=\pm8
.\end{array}
Hence, the solutions are $
x=\{-8,8\}
.$