Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 8^a and y = 7^b, which of the following is a possible units digit of xy?	Choose the correct choice from the following choices: A) 1, 4 B) 4, 1, 2 C) 5, 8 D) 2, 4, 6 and 8 E) 8, 6
Only Units digit of X and Y contribute to the Units digit of XY.   Finding all values ofXfor positive values ofa   When,   a=1; X=8   a=2; X=64   a=3; X=512   a=4; X=2048........ Units digit repeat in a cycle of 8,4,2,8......   Similarly, Finding all values ofYfor positive values ofb   When,   b=1; Y=7   b=2; Y= 49   b=3; Y= 343   b=4; Y=2041   b=5; Y=16807....... Units digit repeat in cycle of 7,9,3,1,7,9,3....   So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y   When X=8 and Y=7: Units digit of XY = 56   When X=8 and Y=9: Units digit of XY = 72   When X=8 and Y=3: Units digit of XY = 24   When X=4 and Y=7: Units digit of XY = 28   When X=4 and Y=9: Units digit of XY = 36   When X=4 and Y=3: Units digit of XY = 12   When X=2 and Y=7: Units digit of XY = 14   When X=2 and Y=9: Units digit of XY = 18   When X=2 and Y=3: Units digit of XY = 6   Only four possibilities for Units digit of XY i.e. 2, 4, 6 and 8   therefore answer is 2, 4, 6 and 8
<result>D</result>
Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 8^a and y = 7^b, which of the following is a possible units digit of xy?