Simplify. Use positive exponents for any variables. Assume that all bases are not equal to 0 \( \frac{p^{-2}}{q^{-9}} \)

To simplify the expression \( \frac{p^{-2}}{q^{-9}} \) and ensure all exponents are positive, follow these steps: 1. **Convert Negative Exponents to Positive:** - Recall that \( a^{-n} = \frac{1}{a^n} \). - Apply this to both \( p^{-2} \) and \( q^{-9} \): \[ \frac{p^{-2}}{q^{-9}} = \frac{\frac{1}{p^2}}{\frac{1}{q^9}} \] 2. **Simplify the Fraction:** - When you divide by a fraction, it's the same as multiplying by its reciprocal: \[ \frac{\frac{1}{p^2}}{\frac{1}{q^9}} = \frac{1}{p^2} \times \frac{q^9}{1} = \frac{q^9}{p^2} \] 3. **Final Simplified Form:** - The expression with all positive exponents is: \[ \frac{q^9}{p^2} \] **Answer:** \(\dfrac{q^{9}}{\,p^{\,2}\,}\)