1. **State the problem:** Express $11^4 \div 11$ in index form. 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. **Final answer in index form:** $$11^3$$