If you only care about the one's digit, it only matters that 513 ends with a 3.

3^0 ends with 1
3^1 ends with 3
3^2 ends with 9
3^3 ends with 7

from here, it repeats: 1, 3, 9, 7. So simply take the power and divide by 4. The remainder should tell you which of these is the last digit.

For your example: 128 mod 4 is 0, therefore 513^128 ends with a 1.

Hope that helps!