If a = 105 and a^3= 21 * 35 * 45 * b, what is the value of b?  Pick:	A) 35	B) 42	C) 45	D) 49	E) 54

Rationale: "first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 35 = 7 * 5 45 = 3 * 3 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 7 * 5 * 3 * 3 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 2 * 7 ^ 2 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 3 * 5 ^ 2 * 7 ^ 2 b = 5 * 7 = 35 correct answer a ."
Answer: A