A student simplified (cube root of 125 − 12 ÷ 2)(4 − 6)2 using the following steps:

Question

(cube root of 125 − 12 ÷ 2)(4 − 6)2

Step 1: (5 − 12 ÷ 2)(4 − 6)2 Simplify the cube root.
Step 2: (−7 ÷ 2) (4 − 6)2 Subtract within first parentheses.
Step 3: −6.5(4 − 6)2 Divide within the first parentheses.
Step 4: −6.5(4 − 36) Simplify the exponent.
Step 5: −6.5(−32) Subtract within the parentheses.
Step 6: 208 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 125 − 12 ÷ 2)(4 − 6)2. (6 points)

Answer 1

Part A: The mistake in Step 2 is that the student subtracted within the first parentheses when they should have multiplied. To correct it, the expression should be multiplied instead of subtracted.

Part B: The mistake in Step 4 is that the student simplified the exponent incorrectly. The exponent should be squared, not subtracted. To correct it, the expression should be squared instead of subtracted.

Part C:

(cube root of 125 − 12 ÷ 2)(4 − 6)2

Step 1: (5 - 12 ÷ 2)(4 - 6)2
Step 2: (5 - 6)(4 - 6)2
Step 3: (-1)(4 - 6)2
Step 4: (-1)(-2)2
Step 5: (-1)(4)
Step 6: -4