20. \( \left(15 p^{5} q r^{7}\right) \cdot\left(\frac{4}{3} p^{2} q r\right) \)

To simplify the expression \( \left(15 p^{5} q r^{7}\right) \cdot\left(\frac{4}{3} p^{2} q r\right) \), let's first multiply the coefficients and then combine the variables. 1. **Multiply the coefficients**: \[ 15 \cdot \frac{4}{3} = 15 \cdot \frac{4}{3} = 15 \div 3 \cdot 4 = 5 \cdot 4 = 20 \] 2. **Combine the variables**: - For \( p \): \( p^{5} \cdot p^{2} = p^{5+2} = p^{7} \) - For \( q \): \( q \cdot q = q^{1+1} = q^{2} \) - For \( r \): \( r^{7} \cdot r = r^{7+1} = r^{8} \) Putting it all together, we get: \[ 20 p^{7} q^{2} r^{8} \] Thus, the simplified expression is: \[ \boxed{20 p^{7} q^{2} r^{8}} \]