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8^8 = (2^3)^8 = 2^24 = 4^12 (I converted it into a base of 4 because finding the units digit in the base of 4 is simple; it is 4 if the power is odd and 6 if the power is even)

units digit of 4^12 = 6
a number with units digit 6 when divided by 2 will give a units digit of 3.