SOLUTION: the last digit of 7^2010 is? how to solve this?and option are a)7 b)9 c)3 d)1

Algebra ->  Square-cubic-other-roots -> SOLUTION: the last digit of 7^2010 is? how to solve this?and option are a)7 b)9 c)3 d)1      Log On


   

Question 590771: the last digit of 7^2010 is? how to solve this?and option are
a)7 b)9 c)3 d)1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
7^1 = 7 ... last digit is 7
7^2 = 49 ... last digit is 9
7^3 = 343 ... last digit is 3
7^4 = 2401 ... last digit is 1
7^5 = 16807 ... last digit is 7


So it repeats every 4 values.

Since 2010/4 = 502 remainder 2, this means that on the 2010th exponent, it will really be at the second stage. Looking above, the second stage has a last digit of 9.

So the last digit of 7%5E%282010%29 is 9