Simplify Exponents 7C5A55

1. **State the problem:** Simplify the expression $$\frac{p^{-8}}{t^{-2}q^{-9}}$$ and write the answer using only positive exponents. 2. **Recall the exponent rules:** - When dividing powers with the same base, subtract exponents: $$a^m / a^n = a^{m-n}$$. - Negative exponents mean reciprocal: $$a^{-m} = \frac{1}{a^m}$$. - To write with positive exponents, move factors with negative exponents from numerator to denominator or vice versa. 3. **Rewrite the expression:** $$\frac{p^{-8}}{t^{-2}q^{-9}} = p^{-8} \times t^{2} \times q^{9}$$ 4. **Move negative exponents to the opposite part of the fraction:** - Since $$p^{-8}$$ is in the numerator, rewrite as $$\frac{1}{p^{8}}$$. - Since $$t^{-2}$$ and $$q^{-9}$$ are in the denominator, rewrite as $$t^{2}$$ and $$q^{9}$$ in the numerator. 5. **Combine all positive exponents:** $$\frac{t^{2} q^{9}}{p^{8}}$$ **Final answer:** $$\boxed{\frac{t^{2} q^{9}}{p^{8}}}$$