(September 26, 2018 at 9:56 pm)Tiberius Wrote:(September 26, 2018 at 9:42 pm)Aliza Wrote: 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.
Hmmmm. A few days ago I was redirected to do it this way, but what you're saying is also making sense. I remember thinking a few days ago, "what the fuck are you talking about?!" But maybe I misunderstood what I was being told and trying to jam this new exponent understanding into my previous understanding shorted out my brain.
Because I sure as hell wasn't going to say to the guy, "Wait, can you explain that to me again. That doesn't make sense."
I've been looking at this way too long... and now I'm all twisted around.
