Fully simplify using only positive exponents. \[ \frac{9 x^{5} y^{3}}{15 x^{3} y^{4}} \]

To simplify the expression \(\frac{9 x^{5} y^{3}}{15 x^{3} y^{4}}\), we can first simplify the coefficients and then deal with the variables separately. 1. Simplify the coefficients: \(\frac{9}{15} = \frac{3}{5}\) 2. Simplify the \(x\) terms: \(\frac{x^{5}}{x^{3}} = x^{5-3} = x^{2}\) 3. Simplify the \(y\) terms: \(\frac{y^{3}}{y^{4}} = y^{3-4} = y^{-1}\) Now, putting it all together, we have: \[ \frac{3}{5} x^{2} y^{-1} \] To express everything with positive exponents, recall that \(y^{-1} = \frac{1}{y}\). Therefore, we rewrite the expression as: \[ \frac{3}{5} x^{2} \cdot \frac{1}{y} = \frac{3 x^{2}}{5 y} \] Thus, the fully simplified expression is: \[ \frac{3 x^{2}}{5 y} \]