Question

Which term in the expansion of $\{{\left(\frac{x}{\sqrt{y}}\right)}^{1/3}+{\left(\frac{y}{x^{1/3}}\right)}^{1/2}\}$ contains $x$ and $y$ to one and the same power?

Answer 1

$\frac{x^{1/3}}{y^{1/6}}+\frac{y^{1/2}}{x^{1/6}}=\frac{x^{1/3}{x}^{1/6}+y^{1/3}{y}^{1/6}}{x^{1/6}{y}^{1/6}}$

$\Rightarrow \frac{x^{\frac{3}{6}}+y^{\frac{3}{6}}}{x^{1/6}{y}^{1/6}}=\frac{x^{1/2}+y^{1/2}}{x^{1/6}{y}^{1/6}}$.