I think i know how to solve it but is that the best way? Is there a better way (using number theory).
What i do is:
knowing that
1st power last digit: 3
2nd power last digit: 9
3rd power last digit: 7
4rh power last digit: 1
5th power last digit: 3
3347=35⋅69+2=(35)69⋅32=3⋅32=33=27 so the result is 7.
Answer
How about
32≡−1(mod10)
so
3347≡32⋅173+1≡3⋅(−1)173≡−3≡7(mod10)
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