Are you working in modular arithmetic? My approach would be to raise 7 to different exponents mod 100, and then multiply them together to get 7^361. Take == to be the modular symbol:

7^4 == 1 (mod 100)

7^8 == 1 (mod 100)

7^16 == 1 (mod 100)

..

You'll get to high exponents very quickly. Since 361 = 256 + 64 + 32 + 8 + 1:

(7^256)(7^64)(7^32)(7^8)(7^1) == 1*1*1*1*7 mod(100) == 7 mod(100)

Hope it helps, and apologize if it's wrong.

EDIT: gave you mod 362 instead of 361