Question

A student simplified (cube root of 64 − 16 ÷ 2)(2 − 4)2 using the following steps: (cube root of 64 − 16 ÷ 2)(2 − 4)2 Step 1: (4 − 16 ÷ 2)(2 − 4)2 Simplify the cube root. Step 2: (−12 ÷ 2)(2 − 4)2 Subtract within 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. (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 64 − 16 ÷ 2)(2 − 4)2. (6 points)

Answer 1

The mistake in Step 2 is dividing -16 by 2.

The mistake in Step 4 is simplifying 2 - 16 as -16.

To simplify (cube root of 64 - 16 ÷ 2)(2 - 4)2, evaluate the expressions inside the parentheses and follow the order of operations.

Step-by-step explanation:

Part A: The mistake in Step 2 is that the student subtracted within the first parentheses instead of dividing.

To correct it, the student should divide -16 by 2, which equals -8.

So the correct step is (-12 ÷ 2)(2 - 4)2.

Part B: The mistake in Step 4 is that the student simplified 2 - 16 as -16 instead of -14.

To correct it, the student should subtract 4 from 16, which equals 12.

So the correct step is -6(2 - 12).

Part C: To simplify (cube root of 64 - 16 ÷ 2)(2 - 4)2, we start by evaluating the expressions inside the parentheses.

The cube root of 64 is 4. Inside the first parentheses, we divide 16 by 2 to get 8.

Inside the second parentheses, we subtract 4 from 2 to get -2.

Now we have 4 - 8(-2)2. Simplifying further, we calculate -2 raised to the power of 2, which is 4.

Then we multiply 8 by 4, which equals 32.

Finally, we subtract 4 from 32 to get the final answer of 28.