express as a quotient with no negative exponents: (-x^2/y)^3 multiplied by (x^-1/2y^2)^2
$\displaystyle \left(\frac{-x^2}{y}\right)^3 \times \left(\frac{x^{-1}}{2y^2}\right)^2$
Remember the property of negative exponents:
$\displaystyle x^{-a} = \frac{1}{x^a}$
$\displaystyle \implies \left(\frac{-x^2}{y}\right)^3 \times \left(\frac{1}{2y^2 \cdot x^{1}}\right)^2$
In case you mean:
(-x^(2) / y)^3 * (x^(-1/2) y^2)^2
$\displaystyle \left(\frac{-x^2}{y}\right)^3 \cdot \left(\frac{x^{-\frac12}}{y^2} \right)^2 = \frac{x^{-6} \cdot x^{-1}}{y^3 \cdot y^4} = \frac1{x^7 \cdot y^7} = \left(\frac1{xy} \right)^7$
Please be so kind and make excessive use of brackets to avoid those ambiguities.