1. **State the problem:** Simplify the expression $$\frac{p^8 p}{p^{-1}}$$ and write the result using positive exponents. 2. **Recall exponent rules:** - When multiplying powers with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$ - When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$ - Negative exponents mean reciprocal: $$a^{-n} = \frac{1}{a^n}$$ 3. **Simplify the numerator:** $$p^8 \cdot p = p^{8+1} = p^9$$ 4. **Rewrite the expression:** $$\frac{p^9}{p^{-1}}$$ 5. **Apply division rule:** $$p^{9 - (-1)} = p^{9+1} = p^{10}$$ 6. **Final answer:** $$p^{10}$$ The expression simplified with positive exponents is $$p^{10}$$.