1. **State the problem:** Simplify the expression $x^{-1} / x^{-2}$. 2. **Recall the rule for division of exponents with the same base:** $$\frac{a^m}{a^n} = a^{m-n}$$ 3. **Apply the rule:** $$\frac{x^{-1}}{x^{-2}} = x^{-1 - (-2)} = x^{-1 + 2}$$ 4. **Simplify the exponent:** $$x^{1} = x$$ 5. **Final answer:** $$x$$ This means dividing $x^{-1}$ by $x^{-2}$ results in $x$ because subtracting the exponents is the key step.