SOLUTION: 5^n+2 - 5^n+3 = -2500, My teacher solved it like this. I don't understand why we separate the 5's in the process and where the second 5^n went. Please explain. 5^n x 5^2 - 5^n x

Algebra ->  Exponents -> SOLUTION: 5^n+2 - 5^n+3 = -2500, My teacher solved it like this. I don't understand why we separate the 5's in the process and where the second 5^n went. Please explain. 5^n x 5^2 - 5^n x      Log On


   

Question 1188422: 5^n+2 - 5^n+3 = -2500, My teacher solved it like this. I don't understand why we separate the 5's in the process and where the second 5^n went. Please explain.
5^n x 5^2 - 5^n x 5^3 = -2500
25 x 5^n - 125 x 5^n = -2500
-100 x 5^n = -2500
5^n = 25
5^n = 5^2
n = 2
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Your teacher made these transformations to have   5%5En   as a new unknown.

The rest of his  (or her)  transformations is totally clear,  as a day light.