Answer
Solutions:
$x=25$
$x=-29$
Work Step by Step
$(x+2)^{\frac{2}{3}}=9~~$ (Cube both sides):
$[(x+2)^{\frac{2}{3}}]^3=9^3$
$(x+2)^2=729$
$x+2=±27$
$x=-2±27$
$x=-2+27=25$
or
$x=-2-27=-29$
Check the solutions:
$x=25$:
$(25+2)^{\frac{2}{3}}=(\sqrt[3] {27})^2=3^2=9$
$x=25$:
$(-29+2)^{\frac{2}{3}}=(\sqrt[3] {-27})^2=(-3)^2=9$
