1. **State the problem:** Simplify the expression $x \cdot x^{-3}$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying powers with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$ 3. **Apply the rule:** Here, the base is $x$, and the exponents are $1$ (since $x = x^1$) and $-3$. So, $$x \cdot x^{-3} = x^{1 + (-3)} = x^{-2}$$ 4. **Interpret the result:** A negative exponent means the reciprocal, so $$x^{-2} = \frac{1}{x^2}$$ 5. **Final answer:** $$x \cdot x^{-3} = \frac{1}{x^2}$$