If a and b are integers and (2^a)(3^b) is a factor of 90^40, what is the largest possible value of ab?	Select the correct option:
A) 2a  B) 5a  C) 20a  D) 40a  E) 80a
(2^a)(3^b) is a factor of 90^40   We need to find the largest possible value of ab.   We know that 90 = 2^1*5^1*3^2   Therefore 90^40 will have 2 powers of 3 in it.   Hence in (2^a)(3^b), b has to 2   Therefore value of ab = 2a   Correct Option: 2a
<result>A</result>
If a and b are integers and (2^a)(3^b) is a factor of 90^40, what is the largest possible value of ab?