1. **State the problem:** Simplify the expression $(x+1)^{30}$. 2. **Formula used:** The expression is a binomial raised to a power. The binomial theorem states: $$ (a+b)^n = \sum_{k=0}^n \binom{n}{k} a^{n-k} b^k $$ where $\binom{n}{k}$ is the binomial coefficient. 3. **Explanation:** Here, $a = x$, $b = 1$, and $n = 30$. Expanding fully would be lengthy, but the expression is already simplified as a power. 4. **Intermediate work:** No further simplification is possible without expansion. 5. **Final answer:** The expression is simplified as: $$ (x+1)^{30} $$ This is the simplest form unless expansion is requested.