Answers

2015-08-20T20:46:27+05:30
1) look for the pattern as we increase the exponent
     2 power1 = 2 (units digit is 2 )
     2 power 2 = 4 (units digit is 4 )  and so on

2 power 1 has units digit 2
2 power 2 has units digit 4
2 power 3 has units digit 8
2 power 4 has units digit 6
2 power 5 has units digit 2
2 power 6 has units digit 4

here we can see it repeats for every 4 times
whenever n is multiple of 4 the unts digit of 2 power n is 2
that is
2 power 4 has units digit 2
2 power 8 has units digit 2 ...etc

As 2012 is multiple of 4
at this point we can find the units digit of 2 power 2012 is 2
                                            units digit of 2 power 2013 is 4
                                            unit digit of 2 power 2014 is 8
                                  and    units digit of 2 power 2015 is 6

therefore units place of 2 power 2015 = 6
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