A student simplified (the cube root of 27 β 12 Γ· 6)(7 β 9)2 using the following steps:
(the cube root of 27 β 12 Γ· 6)(7 β 9)2
Step 1: (3 β 12 Γ· 6)(7 β 9)2 Simplify the cube root.
Step 2: (β9 Γ· 6)(7 β 9)2 Subtract within first parentheses.
Step 3: β1.5(7 β 9)2 Divide within the first parentheses.
Step 4: β1.5(7 β 81) Simplify the exponent.
Step 5: β1.5(β74) Subtract within the parentheses.
Step 6: 111 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 (the cube root of 27 β 12 Γ· 6)(7 β 9)2. (6 points)