1. The problem asks to simplify the expression $5^4 \cdot 5^7$ in exponential form. 2. Recall the rule for multiplying powers with the same base: $$a^m \cdot a^n = a^{m+n}$$ where $a$ is the base and $m,n$ are exponents. 3. Applying this rule to $5^4 \cdot 5^7$, we add the exponents: $$5^{4+7} = 5^{11}$$ 4. Therefore, the simplified exponential form is $5^{11}$. 5. Checking the options given: - Option 1: $5^{28}$ (incorrect) - Option 2: $25^{11}$ (incorrect, base changed) - Option 3: $5^{11}$ (correct) - Option 4: $5^{3}$ (incorrect) Final answer: $5^{11}$ (Option 3)