A student simplified this expression: (3^3 time 3^-2)/ using these steps:
Step 1: (3^-6)/(3^12)
Step 2: (1)/(3^6 times 3^12)
Step 3: (1)/(3^18)
Which of these steps contains a mistake from the previous step?
A: There are no mistakes.
B: Step 1 had the mistake, correct answer to this step is (3^1)/(3^12)
C: Step 2 had the mistake, correct answer to this step is 3^6
D: Step 3 had the mistake, correct answer to this step is (1)/(3^6)
B: Step 1 had the mistake, correct answer to this step is (3^1)/(3^12)
In Step 1, the student simplified (3^3 * 3^-2) incorrectly. According to the rules of exponents, when multiplying with the same base, you add the exponents. So, the correct simplification of (3^3 * 3^-2) is (3^(3-2)), which is equal to 3^1, not 3^-6.