Determine the correct order of operations to solve the equation:
(7) $5+\left(3 \cdot 4^{2}+2\right)$
So, the final answer is \(\boxed{55}\)
Step 1 :First, we need to solve the operation inside the parentheses, which includes an exponent and a multiplication operation. According to the order of operations in mathematics (PEMDAS), we should first calculate the exponent, then the multiplication, and finally the addition.
Step 2 :Calculate the exponent: \(4^{2} = 16\)
Step 3 :Then, multiply 3 by the result of the exponent: \(3 \cdot 16 = 48\)
Step 4 :Add 2 to the result of the multiplication: \(48 + 2 = 50\)
Step 5 :Finally, add 5 to the result of the operation inside the parentheses: \(5 + 50 = 55\)
Step 6 :So, the final answer is \(\boxed{55}\)