You're getting closer

I couldn't think of any clever way to solve this problem. I didn't want to have to find a way to compute 200 digit integers, so I merely expressed them as strings of their prime factors in ascending order, then compared the strings to weed out the duplicates. Example: 84 = 2^2*3*7, so 84^45 = 2^90*3^45*7^45. Each number is expressed uniquely in this way.

Btw, if you want to check your answers log on to projecteuler.net and go to Problem #29.