(September 26, 2018 at 9:42 pm)Aliza Wrote:(September 26, 2018 at 9:33 pm)Tiberius Wrote: I don’t see a 4 in that solution.
In this case however I believe the problem is asking you to prove the general case.
Purplemath factored out the 2 at an earlier stage.
= [2^k+1 – 2] + 2^k+1
I added the 2^k+1 to the other 2^k+1 to give me 4^k+1, and then I factored out the 2 from the remaining two terms.
It is a proof. I'm just trying to get from point A to point B, but I can't for the life of me figure out what exponent rule allows for that. Why if I can factor out a 2 and then redistribute it does it not just go back into the equation without affecting the exponent? I understand that (x^2)(x^2) would be x^(2+2) which would be x^4, but why in the case of my example question, did the exponent not change when I factored out that two as such that it would go up by one when I put the two back in?
My point is that 2^k+1 + 2^k+1 doesn't equal 4^k+1.
Replace k with 1:
2^(1+1) + 2^(1+1) = 4^(1+1)
2^2 + 2^2 = 4^2
4 + 4 = 16
8 = 16.
It doesn't work.
However 2^k+1 + 2^k+1 does equal 2 * 2^k+1, which is where you can factor out the 2. For the same reasons as above, you cannot do 2 * 2^k+1 and get 4^k+1.
