1. **State the problem:** Simplify the expression $$\frac{1}{p^{-1}}$$ and write the result using positive exponents. 2. **Recall the rule for negative exponents:** For any nonzero number $a$ and integer $n$, $$a^{-n} = \frac{1}{a^n}$$. This means a negative exponent indicates the reciprocal. 3. **Apply the rule to the denominator:** Since the denominator is $p^{-1}$, we can rewrite it as $$p^{-1} = \frac{1}{p}$$. 4. **Rewrite the original expression:** $$\frac{1}{p^{-1}} = \frac{1}{\frac{1}{p}}$$ 5. **Simplify the complex fraction:** Dividing by a fraction is the same as multiplying by its reciprocal: $$\frac{1}{\frac{1}{p}} = 1 \times p = p$$ 6. **Final answer:** The expression simplifies to $$p$$, which uses a positive exponent implicitly (since $p = p^1$). Therefore, $$\frac{1}{p^{-1}} = p$$.