To simplify 12 - 2^3 + 4 ÷ 2 + 2^4 using the order of operations (also known as PEMDAS), follow these steps:
1. Start with the exponentiation: 2^3 = 2 * 2 * 2 = 8
The expression now becomes: 12 - 8 + 4 ÷ 2 + 2^4
2. Continue with the exponentiation: 2^4 = 2 * 2 * 2 * 2 = 16
The expression now becomes: 12 - 8 + 4 ÷ 2 + 16
3. Move on to the division: 4 ÷ 2 = 2
The expression now becomes: 12 - 8 + 2 + 16
4. Finally, perform the addition and subtraction from left to right: (12 - 8) + 2 + 16 = 4 + 2 + 16 = 22
Therefore, 12 - 2^3 + 4 ÷ 2 + 2^4 simplifies to 22.