#### Answer

The solutions are $27$ and $125$.

#### Work Step by Step

The given equation can be written as:
$(x^{1/3})^2-8x^{1/3}+15=0$
Let $u=x^{1/3}$.
Rewrite the equation above using $u$ to obtain:
$u^2-8u+15=0$
Factor the trinomial to obtain:
$(u-5)(u-3)=0$
Use the Zero Factor Property by equating each factor to zero, then solve each equation to obtain:
\begin{array}{ccc}
\\&u-5=0 &\text{or} &u-3=0
\\&u=5 &\text{or} &u=3
\end{array}
Since $u=x^{1/3}$, then:
\begin{array}{ccc}
\\&u=5 &\text{or} &u=3
\\&x^{1/3}=5 &\text{or} &x^{1/3}=3
\\&(x^{1/3})^3=5^3 &\text{or} &(x^{1/3})^3=3^3
\\&x=125 &\text{or} &x=27
\end{array}
Therefore, the solutions are $27$ and $125$.