How to Simplify a Series with Basic Algebra?

[kuahji]

$$\sum$$ (2^(2n)-(-7)^n)/(11^n)

The book has that expression equal to
$$\sum$$ (4/11)^n - $$\sum$$ (-7/11)^n

I'm not seeing how the first part changes to (4/11)^n. Wouldn't it be (2^2+2^n) & not 4^n? Or is there something else I'm missing?

 

[nicksauce]

Fact:
$$(x^y)^z = x^{yz}$$.
Does that help you out?

 

[kuahji]

Crude, nm. 2am & math doesn't mix sometimes. ^_^