Simplify Exponents B1Cc19

1. **State the problem:** Simplify the expression $$\frac{p^{-5}}{7^{-2}q^{-9}}$$ and write the answer using only positive exponents. 2. **Recall the exponent rules:** - $a^{-m} = \frac{1}{a^m}$ - $\frac{a^m}{a^n} = a^{m-n}$ - When dividing, negative exponents in the denominator can be moved to the numerator as positive exponents, and vice versa. 3. **Rewrite the expression:** $$\frac{p^{-5}}{7^{-2}q^{-9}} = p^{-5} \times 7^{2} \times q^{9}$$ 4. **Explanation:** - The negative exponent $7^{-2}$ in the denominator moves to the numerator as $7^{2}$. - The negative exponent $q^{-9}$ in the denominator moves to the numerator as $q^{9}$. 5. **Final simplified expression:** $$7^{2} q^{9} p^{-5}$$ 6. **Rewrite $p^{-5}$ with positive exponent:** Move $p^{-5}$ from numerator to denominator: $$\frac{7^{2} q^{9}}{p^{5}}$$ 7. **Calculate $7^{2}$:** $$7^{2} = 49$$ 8. **Final answer:** $$\frac{49 q^{9}}{p^{5}}$$