Final answer:
The student made mistakes in calculating due to misunderstanding of the order of operation rules in mathematics. The correct calculation is (-1)(-2²) which results in -4.
Step-by-step explanation:
The student made mistakes in Step 2 and Step 4. In Step 2, before subtracting, the division operation should be performed due to the order of operations rule (PEMDAS/BODMAS), which stands for Parenthesis, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). So, 5 - 12 ÷ 2 should be 5 - 6 = -1, not -13 ÷ 2 = -6.5.
In Step 4, when squaring -2 (which is the result of 4 - 6), every number squared is always positive. Therefore, (-2)² is 4, not -4. There is a difference between -(2)² and (-2)². In the first, the square applies only to the 2, while in the latter, it applies to -2.
So, steps should be: Step1: (5 - 12 ÷ 2)(4 - 6)² becomes (-1)(-2²). Step2: (-1)(4). Step 3: -4
Learn more about Order of Operations