()) Divide. Simplify your answer. \( \frac{7 q^{2}}{6 p^{2}} \div 15 p^{2} q \)

To simplify the expression: \[ \frac{7 q^{2}}{6 p^{2}} \div 15 p^{2} q \] **Step 1: Rewrite the division as multiplication by the reciprocal** \[ \frac{7 q^{2}}{6 p^{2}} \div 15 p^{2} q = \frac{7 q^{2}}{6 p^{2}} \times \frac{1}{15 p^{2} q} \] **Step 2: Multiply the numerators and the denominators** \[ \frac{7 q^{2} \times 1}{6 p^{2} \times 15 p^{2} q} = \frac{7 q^{2}}{90 p^{4} q} \] **Step 3: Simplify the expression by reducing common factors** - \( q^{2} \) divided by \( q \) is \( q^{1} \) (since \( q^{2} \div q = q^{2-1} = q \)). - The numerical coefficients \( 7 \) and \( 90 \) have no common factors other than 1. \[ \frac{7 q}{90 p^{4}} \] **Final Simplified Answer:** \[ \boxed{\dfrac{7\,q}{90\,p^{4}}} \]