Answer
$\{1,512\}$
Work Step by Step
Step 1. Given the equation $x^{2/3}-9x^{1/3}+8=0$, let $u=x^{1/3}$, we have $u^2-9u+8=0$ which gives $u=1,8$ or $x^{1/3}=1,8$
Step 2. Solve the above equation to get $x= 1,512$ or in set form as $\{1,512\}$