What is the unit's digit of 3127 to the power of 173

3127^173 ≡ 7^173 mod 10

Now - let's look at the powers of 7 mod 10:

7^1 = 7 mod 10

7^2 = 49 ≡ 9 mod 10

7^3 ≡ 3 mod 10

7^4 ≡ 1 mod 10

And this cycle repeats. So

7^173 ≡ 7^1 ≡ 7 mod 10

The last digit is 7.