It appears that you have entered an expression that includes exponents and variables. However, the formatting is unclear due to the way the exponents and variables are laid out.

Let's try to clarify the expression so I can assist you in solving it. Please confirm if this is what you intended:

$\left\{ x^{\frac{2}{3}} \left[ x^{-\frac{3}{1}} y^{-\frac{2}{1}} (x^2 y^{-2})^{-\frac{3}{2}} \right]^{\frac{1}{2}} \right\}^6$

If this looks correct, I can proceed with simplifying it step by step. If not, could you please clarify or reformat the expression?