Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 4^a and y = 3^b, which of the following is a possible units digit of xy? Choices.
A) 1 B) 8 C) 5 D) 7 E) 9
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=4   a=2; X=16   a=3; X=64........ Units digit repeat in a cycle of 4,6,4,6......   Similarly, Finding all values of Y for positive values ofb   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=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   Only four possibilities for Units digit of XY i.e. 4, 2, 8 and 6.   Only 8 is given in answer choices, therefore answer is 8
<result>B</result>
Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 4^a and y = 3^b, which of the following is a possible units digit of xy?