(Order of Operations with Radicals HC)

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)