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When looking for a units digit of a large number, use mod 10
Since a number divisible by 10 ends in 0, the units digit will be the remainder when divided by 10.
Note that 713=23*31
So, we have
Powers of 31 always end in 1 and 23^2 ends in 9
23^2==9(mod 10) and 31==1(mod 10)
The last digit is 9.
The idea with mod arithmetic like this is to break it up into smaller powers to work with.