I think you are taking this problem too complicated.
whenever you see this equation the first thing you must do is simplify the base numbers
if you look at the base numbers they are all powers of 3
so therefore for 9 it is 3^2 so therefore 3^2(3k)
the second step is the 27. 27 is 3^3. so therefore 3^3(3k-1)
since the 3 is already 3 you can leave that alone
for 81 it is 3^4 therefore 3^4(4k)
which finally gives us the equation (3^6k)(3^(9k-3))(3^k) divided by (3^16k)
now that we got all the base numbers to the same number which is 3 simplifying is now very simple
you remove all 3s and simplify as you normally would
therefore
(6k)(9k-3)(k) divided by (16k)
which leaves us with
6k^2(9k-3) divided by 16k
3k(9k-3) divided by 8
^ simplest form
