If a and b are integers and (2^a)(3^b) is a factor of 300^40, what is the largest possible value of ab?  Select.
A) a	B) 5a	C) 20a	D) 40a	E) 80a
(2^a)(3^b) is a factor of 300^40   We need to find the largest possible value of ab.   We know that 300 = 2^2*5^2*3   Therefore 300^40 will have only one power of 3 in it.   Hence in (2^a)(3^b), b has to be 1   Therefore value of ab = a   Correct Option: a
<result>A</result>
If a and b are integers and (2^a)(3^b) is a factor of 300^40, what is the largest possible value of ab?