Question

A student simplified (cube root of 64 - 16 ÷ 2) (2 - 4)^2 using these steps:

step 1: (4 - 16 ÷ 2) (2 - 4)^2 simplify the cube root
step 2: (-12 ÷ 2) (2 - 4)^2 subtract within the 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.
part b: the student made a mistake in step 4. describe the mistake and explain how to correct it.
part c: show every step of your work to simplify (cube root of 64 - 16 ÷ 2)(2 - 4)^2

Answer 1

Answer and Step-by-step explanation:

Part A:

The student made a mistake in **Step 2**. The student subtracted 16 from 4, which is incorrect. The correct operation should be division, as indicated by the original expression (cube root of 64 - 16 ÷ 2). The student should have divided 16 by 2 to get 8, and then subtracted this from 4 (the cube root of 64). So, the correct Step 2 would be: (4 - 8) (2 - 4)^2.

Part B:

The student made a mistake in **Step 4**. The student subtracted 4 from 2, which is incorrect. The correct operation should be squaring, as indicated by the original expression (2 - 4)^2. The student should have squared the result of (2 - 4), which is -2. So, the correct Step 4 would be: -6(-2)^2.

Part C:

Here are the correct steps to simplify the expression (cube root of 64 - 16 ÷ 2)(2 - 4)^2:

1. (4 - 16 ÷ 2) (2 - 4)^2: Simplify the cube root of 64 to 4.

2. (4 - 8) (2 - 4)^2: Divide 16 by 2 to get 8, and subtract it from 4.

3. (-4) (2 - 4)^2: Subtract 8 from 4 to get -4.

4. (-4) (-2)^2: Subtract 4 from 2 to get -2.

5. (-4) * 4: Square -2 to get 4.

6. -16: Multiply -4 and 4 to get -16.

So, the simplified form of the expression (cube root of 64 - 16 ÷ 2)(2 - 4)^2 is -16.