I have seen an example (much simpler) about finding the last digit of..., it uses Fermat's little theorem / Euler's theorem, so I think these theorems might help in our case.

In our case, we are to find the last TWO digits, so I think throughout the entire problem, we should work on mod 100.

By Euler's theorem, 9^40 ≡ 1 (mod 100), but I am not sure how this can help...or is there a better way to solve this problem?

Thanks for any help!

[note: also under discussion in math links forum]