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

(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)

1 answer

Part A: The mistake in Step 2 is when the student subtracted within the parentheses. They subtracted 4 - 6 which is incorrect. To correct it, they should have subtracted 6 - 4 instead, since the order of subtraction matters.

Part B: The mistake in Step 4 is when the student simplified the exponent. They should have squared each term separately, but they squared the entire parentheses. To correct it, they should square each term individually.

Part C:
(cuberoot(125) - 12/2)(4 - 6)^2

Step 1: (5 - 12/2)(4 - 6)^2 Simplify the cube root.
Step 2: (5 - 6)(4 - 6)^2 Simplify the division within the parentheses.
Step 3: (-1)(-2)^2 Simplify the subtraction within the parentheses.
Step 4: (-1)(4) Simplify the exponent.
Step 5: -4 Multiply.

Therefore,
(cuberoot(125) - 12/2)(4 - 6)^2 simplifies to -4.