Final answer:
To simplify the given expressions using the order of operations, follow the steps: 1. For the first expression, simplify the exponent, subtract, multiply, and divide. 2. For the second expression, simplify the exponent, add, and divide. 3. For the third expression, solve the exponent and perform addition and subtraction. 4. For the fourth expression, solve the exponent, multiply, add, and divide.
Step-by-step explanation:
To simplify each expression using the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division [from left to right], and Addition and Subtraction [from left to right]), follow these steps:
- For the first expression (-((3² - 12) × 4) ÷ 2), start by simplifying the exponent within the parentheses: 3² equals 9. Then, subtract 12 to get -3. Next, multiply -3 by 4 to get -12. Finally, divide -12 by 2 to get -6 as the solution.
- For the second expression ((7 × 2²) ÷ (4 + 12)), begin with the exponent within the parentheses: 2² equals 4. Then, add 4 and 12 to get 16. Finally, divide 7 by 16 to get approximately 0.438 as the solution.
- For the third expression (6² + 4 - 3), solve the exponent: 6² equals 36. Then, add 36, 4, and -3 together to get 37 as the solution.
- For the fourth expression (5 + 2² - 3(6)) ÷ 3), calculate the exponent: 2² equals 4. Next, multiply 3 by 6 to get 18. Then, add 5, 4, and -18 together to get -9. Finally, divide -9 by 3 to get -3 as the solution.