Simplify. Expres \( \frac{10 p q \cdot 9 p^{5} q^{3}}{10 p q^{5}} \)

To simplify the expression \( \frac{10 p q \cdot 9 p^{5} q^{3}}{10 p q^{5}} \), we first multiply the terms in the numerator: \( 10 p q \cdot 9 p^{5} q^{3} = 90 p^{6} q^{4} \) Now, the expression becomes: \( \frac{90 p^{6} q^{4}}{10 p q^{5}} \) Next, we can simplify by dividing the coefficients and using the laws of exponents: 1. The coefficients: \( \frac{90}{10} = 9 \) 2. For \( p \): \( \frac{p^{6}}{p} = p^{6-1} = p^{5} \) 3. For \( q \): \( \frac{q^{4}}{q^{5}} = q^{4-5} = q^{-1} = \frac{1}{q} \) Putting all of that together, we have: \( 9 p^{5} \cdot \frac{1}{q} = \frac{9 p^{5}}{q} \) So the simplified expression is: \(\frac{9 p^{5}}{q}\)