To simplify the expression \(2(7^4 + 7)\), we first need to evaluate the terms inside the parentheses:
\(7^4 = 7 \times 7 \times 7 \times 7 = 2401\)
Next, we substitute the value of \(7^4\) back into the expression:
\(2(2401 + 7)\)
Now, we simplify further by adding 2401 and 7:
\(2(2408)\)
Finally, we multiply 2 by 2408:
\(2 \times 2408 = 4816\)
Therefore, \(2(7^4 + 7)\) simplifies to 4816.