Am I wrong, or is it the book?
This simplifies first to (3^-n . 3^4n) / (3^[3n-2] . 3^3). Call this step 1.
Now, if I use the laws of indices to work it out straight from step 1, I get
3^(-n + 4n - [3n - 2] - 3) Step 2
The book gives the answer answer as 1/243, which is 3^-5. That would be correct if, from step 2, I SUBTRACT the 2. I added it because it's subtraction of a negative number. Am I correct, or have I missed something in working out the indices?