If a = 105 and a^3= 21 * 49 * 45 * b, what is the value of b?
Choose the most appropriate option:
A) 25
B) 42
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   49 = 7 * 7   45 = 3 * 3 * 5   so, (105)^3 = 3 * 7 * 7 * 7 * 3 *3 *5 *b   Therefore (3 * 5 * 7) ^ 3 = 3^3 * 5 * 7^3 *b   Therefore, b = 3^3 * 5^3 * 7 ^3/3 ^3 * 5 * 7^3   b = 5^2 = 25   Correct answer 25.
<result>A</result>
If a = 105 and a^3= 21 * 49 * 45 * b, what is the value of b?