If (5!)^2–(4!)^2=2^a3^b13^c and a, b, and c are integers, then what is the value of a + b + c?  Choose the correct choice from the following: A) 12 B) 10 C) 2 D) 1 E) 0
(5!)^2 -(4!)^2=2^a3^b13^c   = [5^2*(4!)^2]-(4!)^2   =[25*(4!)^2]-(4!)^2=24*(4!)^2   = 24*(24^2)=24^3   =[2^3*3]^3=2^9*3^3   so a=9 b=3 c=0   hence a+b+c=9+3+0= 
<gadget id="calculator">9+3+0</gadget>
<output>12</output>
12   answer=12
<result>A</result>
If (5!)^2–(4!)^2=2^a3^b13^c and a, b, and c are integers, then what is the value of a + b + c?