How to simplify equation with exponent?

$$\begin{array}{rcl} 10 &=& x^{\frac{1}{3}}y^{\frac{2}{3}} \qquad | \qquad 1^3\\\\ 10^3 &=& x^{\frac{3}{3}}y^{2\cdot\frac{3}{3}} \\\\ 10^3 &=& xy^2 \\\\ xy^2 &=& 10^3 \\\\ xy^2 &=& 10^2\cdot 10 \qquad | \qquad :x \\\\ y^2 &=& 10^2\cdot \dfrac{10}{x} \qquad | \qquad \sqrt{} \\\\ \mathbf{y} & \mathbf{=} & \mathbf{10\cdot \sqrt{ \dfrac{10}{x} }}\\\\ \end{array}$$