Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 5^a and y = 7^b, which of the following is a possible units digit of xy?  Select the correct option:
A) 1 B) 4 C) 5 D) 7 E) 8
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=5   a=2; X=25   a=3; X=125........ Units digit repeat in a cycle of 5......   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=5 and Y=7: Units digit of XY = 35   When X=5 and Y=9: Units digit of XY = 45   When X=5 and Y=3: Units digit of XY = 15   When X=5 and Y=1: Units digit of XY = 5   Only one possibilities for Units digit of XY i.e. 5   therefore answer is 5
<result>C</result>
Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 5^a and y = 7^b, which of the following is a possible units digit of xy?