#### Answer

The solutions are $x=\sqrt{8}$ and $x=\sqrt{27}$

#### Work Step by Step

$x^{4/3}-5x^{2/3}+6=0\hspace{0.7cm} \color{blue}{\text{Given equation}}$
$W^2-5W+6=0\hspace{3.3cm} \color{blue}{\text{Let } W=x^{2/3}}$
$(W-2)+(W-3)=0\hspace{2.3cm} \color{blue}{\text{Factor}}$
$W-2=0\hspace{0.5cm}or\hspace{0.5cm}W-3=0\hspace{1.3cm} \color{blue}{\text{Zero-Product Property}}$
$W=2\hspace{1.5cm}W=3\hspace{1.99cm} \color{blue}{\text{Solve}}$
Now change $W$ back into the correspondimg values of $x$
$x^{2/3}=2\hspace{1.5cm}x^{2/3}=3$
$x=2^{3/2}\hspace{1.5cm}x=3^{3/2}$
$x=\sqrt{8}\hspace{1.5cm}x=\sqrt{27}$
The solutions are $x=\sqrt{8}$ and $x=\sqrt{27}$