Answer
The solutions are $x=125$ and $x=-8$
Work Step by Step
$x^{2/3}-3x^{1/3}-10=0$
Let $u$ be equal to $x^{1/3}$
If $u=x^{1/3}$, then $u^{2}=x^{2/3}$
Rewrite the original equation using the new variable $u$:
$u^{2}-3u-10=0$
Solve by factoring:
$(u+2)(u-5)=0$
Set both factors equal to $0$ and solve each individual equation for $u$:
$u+2=0$
$u=-2$
$u-5=0$
$u=5$
Substitute $u$ back to $x^{1/3}$ and solve for $x$:
$x^{1/3}=-2$
$x=(-2)^{3}$
$x=-8$
$x^{1/3}=5$
$x=5^{3}$
$x=125$
The solutions are $x=125$ and $x=-8$
