To simplify \( \frac{u^{75}}{y^{30}} \), we notice that it is already in its simplest form.
None of the options provided, such as \( uy^{45} \), \( u^{45} \), \( \frac{u^{75}}{y^{30}} \), or \( 45 \), represent a simplification of this expression.
So the correct response is \( \frac{u^{75}}{y^{30}} \).