A student simplified (cube root of 64 − 16 ÷ 2)(2 − 4)2 using the following steps:

(cube root of 64 − 16 ÷ 2)(2 − 4)2


Step 1: (4 − 16 ÷ 2)(2 − 4)2 Simplify the cube root.
Step 2: (−12 ÷ 2)(2 − 4)2 Subtract within first parentheses.
Step 3: −6(2 − 4)2 Divide within the first parentheses.
Step 4: −6(2 − 16) Simplify the exponent.
Step 5: −6(−14) Subtract within the parentheses.
Step 6: 84 Multiply.


Part A: The student made a mistake in Step 2. Describe the mistake and explain how to correct it. (3 points)

Part B: The student made a mistake in Step 4. Describe the mistake and explain how to correct it. (3 points)

Part C: Show every step of your work to simplify (cube root of 64 − 16 ÷ 2)(2 − 4)2. (6 points)