1. **State the problem:** Simplify the expression $$\frac{x^{11}}{x^4}$$. 2. **Recall the rule for dividing powers with the same base:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Apply the rule:** $$\frac{x^{11}}{x^4} = x^{11-4}$$. 4. **Simplify the exponent:** $$x^{11-4} = x^7$$. 5. **Final answer:** $$x^7$$. This means dividing $x^{11}$ by $x^4$ results in $x^7$ because you subtract the exponents when the bases are the same.