If a = 105 and a^3= 21 * 25 * 15 * b, what is the value of b?
Choices
A) 35 B) 42 C) 45 D) 147 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   15 = 3 * 5   so, (105)^3 = 3 * 7 * 5 * 5 *3 *5 *b   Therefore (3 * 5 * 7) ^ 3 = 3^2 * 5^3 * 7 *b   Therefore, b = 3^3 * 5^3 * 7 ^3/3 ^2 * 5 ^3 * 7   b = 3*7^2 =3* 49= 
<gadget id="calculator">3* 49</gadget>
<output>147</output>
147   Correct answer 147.
<result>D</result>
If a = 105 and a^3= 21 * 25 * 15 * b, what is the value of b?