a student simplified this expression: 3^3 x 3^-2/(3^6)^2 using three steps.

Question

step one- 3^-6/3^12

Step 2- 1/3^6 x 3^12

Step 3- 1/3^18

with of these steps contains a mistake from the previous step

Answer 1

Step 2 contains a mistake from the previous step.

The correct step 2 should be:

Step 2 - (3^3 x 3^-2) / (3^6)^2 = (3^3 x 3^-2) / 3^12

Here, we need to apply the exponent rule that states: (a^m)^n = a^(m x n).

So, the correct step 2 should be:

(3^3 x 3^-2) / 3^12 = (3^3 x 3^-2) / 3^12 = 3^(3 - 2 - 12) = 3^-11.