Question

A student simplified (cube root of 27 − 14 ÷ 2)(6 − 8)2 using the following steps: (cube root of 27 − 14 ÷ 2)(6 − 8)2 Step 1: (3 − 14 ÷ 2)(6 − 8)2 Simplify the cube root. Step 2: (−11 ÷ 2) (6 − 8)2 Subtract within first parentheses. Step 3: −5.5(6 − 8)2 Divide within the first parentheses. Step 4: −5.5(6 − 64) Simplify the exponent. Step 5: −5.5(−58) Subtract within the parentheses. Step 6: 319 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 27 − 14 ÷ 2)(6 − 8)2. (6 points)

Answer 1

The student made mistakes in Step 2 and Step 4. In Step 2, the subtraction should have been done after the division. In Step 4, the exponent should have been simplified correctly. To simplify the expression, first simplify the cube root, then divide, subtract, and raise to the power as needed.

Step-by-step explanation:

Part A: The mistake in Step 2 is the subtraction within the first parentheses. The correct step should be (3 - 7) instead of (3 - 14 ÷ 2), since the division should be done before the subtraction. Therefore, the correct step should be (-4) instead of (-11 ÷ 2).

Part B: The mistake in Step 4 is the simplification of the exponent. The correct exponent should be 2 instead of -2, since raising a negative number to an even power results in a positive number. Therefore, the correct step should be (-5.5)(6 - 8)2 instead of (-5.5)(6 - 64).

Part C: To simplify (cube root of 27 - 14 ÷ 2)(6 - 8)2, follow these steps:

1. Simplify cube root of 27 as 3.
2. Divide 14 ÷ 2 to get 7.
3. Subtract 7 from 3 to get -4.
4. Raise (6 - 8) to the power of 2 to get 4.
5. Multiply -4 by 4 to get -16.

The final result is -16.