#### Answer

$x=\{-1024,1024\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
x^{2/5}=16
,$ raise both sides to the $5$th 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 fifth power, the equation above is equivalent to
\begin{array}{l}\require{cancel}
\left( x^{\frac{2}{5}} \right)^{5}=(16)^{5}
\\\\
x^2=16^{5}
.\end{array}
Taking the square root of both sides and simplifying the radical, the solutions are
\begin{array}{l}\require{cancel}
x=\pm\sqrt{16^5}
\\\\
x=\pm\left(\sqrt{16}\right)^5
\\\\
x=\pm\left(\sqrt{(4)^2}\right)^5
\\\\
x=\pm\left(4\right)^5
\\\\
x=\pm1024
.\end{array}
Hence, the solutions are $
x=\{-1024,1024\}
.$