1. **State the problem:** Multiply $x^{-2}$ by $x^{-3}$. 2. **Recall the rule for multiplying powers with the same base:** $$x^a \times x^b = x^{a+b}$$ This means when multiplying powers with the same base, you add the exponents. 3. **Apply the rule:** $$x^{-2} \times x^{-3} = x^{-2 + (-3)} = x^{-5}$$ 4. **Interpret the result:** A negative exponent means the reciprocal, so: $$x^{-5} = \frac{1}{x^5}$$ **Final answer:** $$x^{-2} \times x^{-3} = x^{-5} = \frac{1}{x^5}$$