If a and b are positive integers and x = 4^a and y = 9^b, which of the following is a possible units digit of xy?
1
4
5
7
8
1
4
5
7
8
x= 4^a = (2^2)^a= (2^a)^2
similarly y = 9^b = (3^b)^2
since a^2 * b^2 = (a*b)^2
Hence xy can be thought of as (2^a*3^b)^2
Additionally if you look at the basic squares ,
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 47
8^2 = 64
9^2 = 81
10^2 = 100
you can have 1 in the units digit when 2^a*3^b either equates to 1 or 9 . So A can be eliminated.
B is possible when a = 1 and b = 2 or vice versa.
C can be eliminated due to the same reason as A being eliminated.
you can eliminate D and E as non of the basic squares have 7 or 8 in their units digit.
Hence B is the ANSWER
