Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 2^a and y = 3^b, which of the following is a possible units digit of xy?  Choices:
A) 4, 2, 8, 6
B) 4 and 2
C) 2 and 8 only
D) 6 and 4
E) 8 and 6
Only Units digit of X and Y contribute to the Units digit of XY.   Finding all values of X for positive values of a   When,   a=1; X=2   a=2; X=4   a=3; X=8   a=4; X=16   a=5; x=32........ Units digit repeat in a cycle of 2,4,8,6,2,4......   Similarly, Finding all values of Y for positive values of b   When,   b=1; Y=3   b=2; Y= 9   b=3; Y= 27   b=4; Y=81   b=5; Y=243....... Units digit repeat in cycle of 3,9,7,1,3,9....   So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y   When X=2 and Y=3: Units digit of XY = 6   When X=2 and Y=9: Units digit of XY = 18   When X=2 and Y=7: Units digit of XY = 14   When X=2 and Y=1: Units digit of XY = 2   When X=4 and Y=3: Units digit of XY = 12   When X=4 and Y=9: Units digit of XY = 36   When X=4 and Y=7: Units digit of XY = 28   When X=4 and Y=1: Units digit of XY = 4   When X=8 and Y=3: Units digit of XY = 24   When X=8 and Y=9: Units digit of XY = 72   When X=8 and Y=7: Units digit of XY = 56   When X=8 and Y=1: Units digit of XY = 8   When X=6 and Y=3: Units digit of XY = 18   When X=6 and Y=9: Units digit of XY = 54   When X=6 and Y=7: Units digit of XY = 42   When X=6 and Y=1: Units digit of XY = 6   There are 4 possibilities for Units digit of XY i.e. 4, 2, 8 and 6   4, 2, 8, 6ns: 4, 2, 8, 6
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Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 2^a and y = 3^b, which of the following is a possible units digit of xy?