Answer
$x=8$, $x=64$
Work Step by Step
$x^{2/3}-6x^{1/3}=-8$
$y=x^{1/3}$
$x^{2/3}-6x^{1/3}=-8$
$(x^{1/3})^{2}-6x^{1/3}=-8$
$(y)^{2}-6(x^{1/3})=-8$
$(y)^{2}-6y=-8$
$y^2-6y=-8$
$y^2-6y+8=-8+8$
$y^2-6y+8=0$
$(y-4)(y-2)=0$
$y-4=0$
$y-4+4=0+4$
$y=4$
$y-2=0$
$y-2+2=0$
$y=2$
$y=x^{1/3}$
$y=4$
$4=x^{1/3}$
$4^3=(x^{1/3})^3$
$64=x$
$y=x^{1/3}$
$y=2$
$2=x^{1/3}$
$2^3=(x^{1/3})^3$
$8=x$
