Lining up A to H (2)

[Milanproda1]

Hi guys, I am confused as to how the exponents are solved in this question:

MGMAT CAT
Question name: Lining up A to H (2)
Difficulty: 600-700
Question Type: PS
Topics Tested: Exponents and Roots

Question:

The integers A, B, C, and D shown on the number line above are all equally spaced. If C and D are equal to 5^12 and 5^13, respectively, what is the value of A?

A- 5^11
B- 5^10
C- -5^12
D- (-7)5^12
E- (-12)5^13

MGMAT ANSWER:


The distance between C and D is 5^13 - 5^12. The distance between any two consecutive points is constant, so the distance between A and D will be 3 times the distance between C and D, or 3(5^13 - 5^12).

The value of A, therefore, will be equal to the value of D minus the distance from A to D:

5^13 - 3(5^13 - 5^12)
5^13 - 3[5^12(5 - 1)]
5^13 - 3(5^12)(4)
5(5^12)- 12(5^12)
(-7)5^12

I am not sure how the exponents were broken down, especially the way in which 5^13 was factored. If anyone can please help me out with an explanation on how to break down these exponents and if there are any rules that I should know.


Thanks!

Milan

[Milanproda1]

NO HELP? =(

[jnelson0612]

Milan,
Here is an almost identical problem--read Ron's explanation, and if you need further help let us know. Thanks!
a-b-c-d-e-f-g-and-h-are-all-integers-t4490.html