Part A: The mistake in Step 2 is that the student incorrectly subtracted the division of 16 ÷ 2 from 4, resulting in a subtraction of 4 - 8 instead of 4 - 2. To correct this, the student should subtract 2 from 4, which gives a result of 2. Therefore, the correct calculation for Step 2 is (4 - 2)(2 - 4)².
Part B: The mistake in Step 4 is that the student incorrectly simplified the exponent 2² to 16. The correct simplification of (2 - 4)² is (-2)², which equals 4. Therefore, the correct calculation for Step 4 is (-6 * 4).
Part C: To simplify (cube root of 64 - 16 ÷ 2)(2 - 4)², we follow the order of operations. Step 1: Simplify the cube root of 64, which equals 4. Step 2: Subtract 16 ÷ 2, which equals 8. So now the expression becomes (4 - 8)(2 - 4)². Step 3: Subtract within the first parentheses, giving us (-4)(2 - 4)². Step 4: Simplify the exponent within the second parentheses. (-4)(-2)² becomes (-4)(4). Step 5: Multiply -4 by 4, giving us -16. Therefore, the simplified expression is -16.
Final answer is In Step 2, the student made a mistake by subtracting the incorrect value. The mistake in Step 4 is an incorrect simplification of the exponent. To simplify (cube root of 64 - 16 ÷ 2)(2 - 4)², the cube root of 64 is simplified to 4, and the expression is evaluated following the order of operations.