If a = 105 and a^3= 21 * 25 * 315 * b, what is the value of b?  Choices:
A) 35
B) 7
C) 45
D) 49
E) 54
First step will be to break down all the numbers into their prime factors.   105 = 3 * 5 * 7   21 = 7 * 3   25 = 5 * 5   315 = 3 * 3 * 5*7   so, (105)^3 = 3 * 7 * 5 * 5 * 3 *3 *5*7 *b   Therefore (3 * 5 * 7) ^ 3 = 3^3 * 5^3 * 7^2 *b   Therefore, b = 3^3 * 5^3 * 7 ^3/3 ^3 * 5 ^3 * 7^2   b = 7   Correct answer 7.
<result>B</result>
If a = 105 and a^3= 21 * 25 * 315 * b, what is the value of b?