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student simplified (the cube root of 125 − 14 ÷ 2)(3 − 5)2 using the following steps:

(the cube root of 125 − 14 ÷ 2)(3 − 5)2
Step 1: (5 − 14 ÷ 2)(3 − 5)2 Simplify the cube root.
Step 2: (−9 ÷ 2)(3 − 5)2 Subtract within first parentheses.
Step 3: −4.5(3 − 5)2 Divide within the first parentheses.
Step 4: −4.5(3 − 25) Simplify the exponent.
Step 5: −4.5(−22) Subtract within the parentheses.
Step 6: 99 Multiply.

Part A: The student subtracted in Step 1 to get Step 2. Why was this a mistake and what should they have done instead? (3 points)
Part B: The student squared one of the numbers in parentheses in Step 3 to get Step 4. Why was this a mistake and what should they have done instead? (3 points)
Part C: Show every step of your work to simplify (the cube root of 125 − 14 ÷ 2)(3 − 5)2. (6 points

Sagot :

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