SOLUTION: If a and b are different prime numbers how many factors does (a^3b^5)^4 have?

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Question 829244: If a and b are different prime numbers how many factors does (a^3b^5)^4 have?
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%5E3b%5E5%29%5E4%22%22=%22%22a%5E12b%5E20

Every factor will be of the form 

a%5Em%2Ab%5En where m=0,1,2,...,12 and n=0,1,2,...,20

For each of the 13 exponents we can choose for m,
there are 21 exponents we can choose for n.

Answer 13×21 = 273 factors

Edwin