Answer
$x=-8, 64$
Work Step by Step
$x^{2/3}-2x^{1/3}-8=0$
$(x^{1/3})^2-2x^{1/3}-8=0$
$x^{1/3} =y$
$(x^{1/3})^2-2x^{1/3}-8=0$
$y^2-2y-8=0$
$(y-4)(y+2)=0$
$y-4=0$
$y=4$
$y+2=0$
$y=-2$
$x^{1/3} =y$
$x^{1/3} =4$
$(x^{1/3})^3 =4^3$
$x=64$
$x^{1/3} =y$
$x^{1/3} =-2$
$(x^{1/3})^3 =(-2)^3$
$x=-8$