Simplify the expression completely: \( \frac{38 x^{16} y^{13}}{20 x^{8} y^{5}} \)

To simplify the expression \( \frac{38 x^{16} y^{13}}{20 x^{8} y^{5}} \), we start by simplifying the coefficients and the variables separately. 1. **Simplifying the coefficients**: The coefficients are \( \frac{38}{20} \). Both numbers can be divided by 2, giving: \[ \frac{38 \div 2}{20 \div 2} = \frac{19}{10} \] 2. **Simplifying the variable \( x \)**: For the \( x \) terms, we have: \[ \frac{x^{16}}{x^{8}} = x^{16 - 8} = x^{8} \] 3. **Simplifying the variable \( y \)**: For the \( y \) terms, we have: \[ \frac{y^{13}}{y^{5}} = y^{13 - 5} = y^{8} \] Now we can combine everything together: \[ \frac{38 x^{16} y^{13}}{20 x^{8} y^{5}} = \frac{19}{10} x^{8} y^{8} \] Thus, the fully simplified expression is: \[ \frac{19 x^{8} y^{8}}{10} \]