1. The problem is to calculate the value of $7^4 + 7^5$. 2. Recall the properties of exponents: $a^m \times a^n = a^{m+n}$ and $a^m + a^n$ cannot be simplified by exponent rules unless factored. 3. Calculate each term separately: - $7^4 = 7 \times 7 \times 7 \times 7 = 2401$ - $7^5 = 7 \times 7 \times 7 \times 7 \times 7 = 16807$ 4. Add the two results: $$7^4 + 7^5 = 2401 + 16807 = 19208$$ 5. Therefore, the final answer is $19208$.