1. **State the problem:** Calculate $11^4 \div 11$. 2. **Recall the exponent division rule:** When dividing powers with the same base, subtract the exponents: $$a^m \div a^n = a^{m-n}$$ 3. **Apply the rule:** Here, the base is 11, $m=4$, and $n=1$, so: $$11^4 \div 11 = 11^{4-1} = 11^3$$ 4. **Calculate $11^3$:** $$11^3 = 11 \times 11 \times 11 = 1331$$ 5. **Final answer:** $$11^4 \div 11 = 1331$$