Simplify \( \frac{25 x^{9} y^{4}}{15 x^{6} y^{8}} \)

To simplify the expression \( \frac{25 x^{9} y^{4}}{15 x^{6} y^{8}} \), follow these steps: 1. **Simplify the Coefficients:** \[ \frac{25}{15} = \frac{5}{3} \] 2. **Simplify the \( x \)-terms using the rule \( \frac{x^a}{x^b} = x^{a-b} \):** \[ \frac{x^9}{x^6} = x^{9-6} = x^3 \] 3. **Simplify the \( y \)-terms using the same rule:** \[ \frac{y^4}{y^8} = y^{4-8} = y^{-4} = \frac{1}{y^4} \] 4. **Combine all the simplified parts:** \[ \frac{5}{3} \times x^3 \times \frac{1}{y^4} = \frac{5x^3}{3y^4} \] **Final Simplified Expression:** \[ \frac{5x^3}{3y^4} \]