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I just want to clear up something to do with factorising indices. Can someone just spend a little time for me :)

Mathematics
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Which term would you factor out? Because you can take out 2^2n or 2^n-1. Which one should you take out? Or its just random \[\huge\frac{2^{2n}-2^{n-1} }{ 2^{n}-2^{-1} }\]
for the numerator it would be \[\huge2^{2n}(1 - 2^{-n-1})\] Would it?
What if you factor out just \(2^n\)

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well ill try |dw:1359854348941:dw| this is right?
|dw:1359854381094:dw|
\[ \huge\frac{2^{2n}-2^{n-1} }{ 2^{n}-2^{-1} } \] \[ \huge\frac{2^n(2^{n}-2^{-1} )}{ 2^{n}-2^{-1} } \]
oh yes thats right :)
so how did you know to factor out 2^n? You just looked at it?
I wanted something similar to the bottom.
so you keep thinking of a number to factor out till you can simplify?
you should be able to think a good number to factor out when you have experience :)

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