1. **State the problem:** Simplify the expression $$\frac{x^6}{x^7}$$ using properties of exponents. 2. **Recall the quotient of powers rule:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$ 3. **Apply the rule:** $$\frac{x^6}{x^7} = x^{6-7}$$ 4. **Simplify the exponent:** $$x^{-1}$$ 5. **Interpret negative exponent:** $$x^{-1} = \frac{1}{x}$$ **Final answer:** $$\frac{x^6}{x^7} = \frac{1}{x}$$