Explanation:

Any odd number raised to a power, which is a multiple of 4, will always give 1 as the unit digit.
Now, 256 is a multiple of 4.
Thus, the last digit in the expansion of 17²⁵⁶ is 1.
Trick:
Last digit = Unit digit of (7 Remainder obtained when 256 divided by 4) = Unit digit of (70)=1