#### Answer

The solutions are $-8$ and $64$.

#### Work Step by Step

The given equation can be written as:
$(x^{1/3})^2-2x^{1/3}-8=0$
Let $u=x^{1/3}$.
Rewrite the equation above using $u$ to obtain:
$u^2-2u-8=0$
Factor the trinomial to obtain:
$(u-4)(u+2)=0$
Use the Zero Factor Property by equating each factor to zero, then solve each equation to obtain:
\begin{array}{ccc}
\\&u-4=0 &\text{or} &u+2=0
\\&u=4 &\text{or} &u=-2
\end{array}
Since $u=x^{1/3}$, then:
\begin{array}{ccc}
\\&u=4 &\text{or} &u=-2
\\&x^{1/3}=4 &\text{or} &x^{1/3}=-2
\\&(x^{1/3})^3=4^3 &\text{or} &(x^{1/3})^3=(-2)^3
\\&x=64 &\text{or} &x=-8
\end{array}
Therefore, the solutions are $-8$ and $64$.