Answer
The solutions are $x=-60$ and $x=68$
Work Step by Step
$(x-4)^{2/3}=16$
Raise both sides to $\dfrac{3}{2}$:
$[(x-4)^{2/3}]^{3/2}=16^{3/2}$
$x-4=\sqrt{16^{3}}$
Simplify the right side:
$x-4=\pm\sqrt{4096}$
$x-4=\pm64$
Solve for $x$:
$x=4\pm64$
The solutions are:
$x=4+64=68$
$x=4-64=-60$
