Answer
The solutions are $x=3$ and $x=-13$
Work Step by Step
$(x+5)^{2/3}=4$
Raise both sides of the equation to $\dfrac{3}{2}$:
$[(x+5)^{2/3}]^{3/2}=4^{3/2}$
$x+5=\pm\sqrt{4^{3}}$
Simplify the right side of the equation:
$x+5=\pm\sqrt{4^{2}\cdot4}$
$x+5=\pm(4)(2)$
$x+5=\pm8$
Solve for $x$:
$x=-5\pm8$
The solutions are:
$x=-5+8=3$
$x=-5-8=-13$
