Question

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

Answer 1

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
\[\huge\frac{2^{2n}-2^{n-1} }{ 2^{n}-2^{-1} }\]

Answer 2

for the numerator it would be
\[\huge2^{2n}(1 - 2^{-n-1})\]
Would it?

Answer 3

What if you factor out just \(2^n\)

Answer 4

well ill try

this is right?

Answer 5

\[
\huge\frac{2^{2n}-2^{n-1} }{ 2^{n}-2^{-1} }
\]

\[
\huge\frac{2^n(2^{n}-2^{-1} )}{ 2^{n}-2^{-1} }
\]

Answer 6

oh yes thats right :)

Answer 7

so how did you know to factor out 2^n?
You just looked at it?

Answer 8

I wanted something similar to the bottom.

Answer 9

so you keep thinking of a number to factor out till you can simplify?

Answer 10

you should be able to think a good number to factor out when you have experience :)