How can exponents be simplified?

[Thunderer]

Well here is the beginning of it:

[-6(-4)^(n-1)] - 9 + [8(-4)^(n-2)] + 12

This is suppose to simplify to 2(-4)^2 + 3.

But I have no idea how that 2(-4)^2 was obtained. Could anybody explain how that would work?

 

[Gale]

i'm going to assume you meant 2(-4)^n not ^2, because otherwise you'd've simplified further, and besides, ^n is the correct answer. do you know how exponentials work and how to factor? that's all they did, and then simplified.

use these rules:

X^(a+b) = (X^a)(X^b)
and by that:
X^(a+b) + X^(a+c) = X^a(X^b + X^c)

 

[HallsofIvy]

It also helps to know that 4= 2^2!