You are working in the ring of integers mod 12. In this ring 3^3 is the same as 3, because 27 = 24 + 3 = 2*12 + 3.
Therefore, since 3^3 = 3 in that ring, anything at all containing 3^3 can be rewritten to use 3 instead of 27.
If you want to think of it more formally, the equivalence class of 3^3 is the same as the equivalence class of 3. Since the ring operations are well-defined, i.e. invariant under choice of representatives of equivalence classes, it doesn't matter which representative of the common equivalence class of 3 and 27 you use. In this case, it makes sense to take a representative with small absolute value--I'm sure it's clear why.
Last edited by prong
on Wed Dec 22, 2010 7:21 am, edited 1 time in total.