Es gilt dass $$\sqrt[n]{x}=x^{\frac{1}{n}}$$
Wir haben also folgendes:
$$\sqrt[3]{x^2y\sqrt{xy^{-1}}}=\sqrt[3]{x^2y\left(xy^{-1}\right)^{\frac{1}{2}}}=\sqrt[3]{x^2y\left(x\right)^{\frac{1}{2}}\left(y^{-1}\right)^{\frac{1}{2}}}=\left(x^2y\left(x\right)^{\frac{1}{2}}\left(y^{-1}\right)^{\frac{1}{2}}\right)^{\frac{1}{3}}=x^{\frac{2}{3}}y^{\frac{1}{3}}x^{\frac{1}{6}}y^{-\frac{1}{6}}=x^{\frac{2}{3}+\frac{1}{6}}y^{\frac{1}{3}-\frac{1}{6}}$$
