10 POINTS! I understand the exponent part but where did the 8 come from and what happen to 7 and 14

http://www.flickr.com/photos/35618868@N0…

#32 is the problem, A is the answer.

The 7 and 14 get reduced. They have a common factor of 7. So, the 14 becomes a 2 and the 7 becomes a 1. Then, when you do out the problem from there, the 2 becomes an 8. This is because you are cubing (multiplying itself three times) the problem. So, 2 times itself 3 times equals 8. 2*2*2=8. That is what happens to the 14 and 7 and how they get the 8.

[(14t^3)/(7s^4)]^3
eliminating 7 between 14 and 7
= [(2t^3)/(s^4)]^3 distributing the power 3
= (2^3 * t^9)/(s^12)
= (8 t^9) / (s^12)

[14t^3/7s^4]^3 =
Well, first cancel the 7 top and bottom to get
[2t^3/s^4]^3 = 2^3 t^[3*3] /s^12 = 8t^9/s^12

(14t^3)^3 = 14^3 * t^9
(7s^4)^3 = 7^3 * s^12

(14t^3)^3 / (7s^4)^3 = [(t^9)/(s^12) ]* [(14*14*14) / (7*7*7)]
= 2*2*2 * [(t^9)/(s^12) ] = 8 [(t^9)/(s^12)] = 8(t^9)/(s^12)

hope that helped

Hmmm that is a toughie ask yo teacha dawg. JK