1. **State the problem:** Simplify the expression $P^{x-1} P^{x+1}$. 2. **Recall the exponent multiplication rule:** When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$ 3. **Apply the rule:** Here, the base is $P$, so $$P^{x-1} P^{x+1} = P^{(x-1) + (x+1)}$$ 4. **Simplify the exponent:** $$(x-1) + (x+1) = x - 1 + x + 1 = 2x$$ 5. **Final simplified expression:** $$P^{2x}$$ This means the product of $P^{x-1}$ and $P^{x+1}$ simplifies to $P^{2x}$ by adding the exponents when multiplying powers with the same base.