A student simplified this expression: (3^3⋅ 2^−4)^4/3^6 using these steps:

Question

Step 1: 3^12 ⋅ 2^−16/3^6
Step 2: 3^6/2^16
Step 3: Answer is 0.011 (1 point) Responses

There is no mistake. The answer is correct.

Step 1 had the mistake. It should have been (6^−4)^4/3^6

Step 2 had the mistake. It should have been 3^2 =9

Step 3 had the mistake. It should have been 3 − 2 = 1^−2 = 1

Answer 1

The correct simplification of the expression is:

Step 1: (3^3 ⋅ 2^−4)^4/3^6
Step 2: (6^−4)^4/3^6
Step 3: 6^−16/3^6
Step 4: 1/2^16
Step 5: 1/65536

Therefore, the correct answer is 1/65536 or approximately 0.0000153.