smc

We see that this fraction can easily be factored as $\frac{x^y}{y^y}\times \frac{y^x}{x^x}$. Since $\frac{y^x}{x^x}=\frac{x^{-x}}{y^{-x}}$, this fraction is equivalent to ${\left(\frac{x}{y}\right)}^y\times {\left(\frac{x}{y}\right)}^{-x}={\left(\frac{x}{y}\right)}^{y-x}$, which corresponds to answer choice $\boxed{(\frac{x}{y}{)}^{y-x}}$.