1. **State the problem:** Simplify the expression $$\frac{2x^{-2}}{2x}$$. 2. **Recall the rules:** - When dividing terms with the same base, subtract the exponents: $$a^m \div a^n = a^{m-n}$$. - Negative exponents mean reciprocal: $$x^{-n} = \frac{1}{x^n}$$. 3. **Simplify the coefficients:** $$\frac{2}{2} = 1$$. 4. **Simplify the variable part using exponent rules:** $$x^{-2} \div x^1 = x^{-2-1} = x^{-3}$$. 5. **Write the final simplified expression:** $$x^{-3} = \frac{1}{x^3}$$. **Answer:** $$\frac{2x^{-2}}{2x} = \frac{1}{x^3}$$.