If a = 105 and a^3= 21 * 25 * 35 * b, what is the value of b?  Choose the correct choice from the following choices:  A) 35  B) 42  C) 45  D) 49  E) 63
First step will be to break down all the numbers into their prime factors.   105 = 3 * 5 * 7   21 = 7 * 3   25 = 5 * 5   35 = 7 * 5   so, (105)^3 = 3 * 7 * 5 * 5 * 7 *5 *b   Therefore (3 * 5 * 7) ^ 3 = 3 * 5^3 * 7^2 *b   Therefore, b = 3^3 * 5^3 * 7 ^3/3 * 5 ^3 * 7^2   b = 3^2*7 = 9*7= 
<gadget id="calculator">9*7</gadget>
<output>63</output>
63   Correct answer 63.
<result>E</result>
If a = 105 and a^3= 21 * 25 * 35 * b, what is the value of b?