How does (1t^(1/2)+0)(t^n) = t^((2n+1)/2) ?

[Four Muffins]

Hello. I'm trying to use the product rule on f(t)= (at^(1/2)+b)t^n. When I do, I end up here, and don't know how to proceed.



The question in the title was prompted by this correction to the exercise I failed. It seems to me that with the suggested substitutions the function should equal t^(n+1/2), not t^((2n+1)/2).




I also asked this question on Quora (but got locked by a moderator pretty quickly so I Googled my way here), and I don't understand how the answerer was able to combine the terms in second last line, it seems like an n disappeared. His answer also seems different to the one in the exercise.



Between the different answers, n+(1/2) and 2n+1 seem interchangeable. This looks similar to what I'd do when I'd find a fraction when using the quadratic equation. I don't think I know why that works, only that it does. Is it a similar thing here?

 

[BigBeachBanana]

Hello. I'm trying to use the product rule on f(t)= (at^(1/2)+b)t^n. When I do, I end up here, and don't know how to proceed.

View attachment 33248

The question in the title was prompted by this correction to the exercise I failed. It seems to me that with the suggested substitutions the function should equal t^(n+1/2), not t^((2n+1)/2).


View attachment 33249

I also asked this question on Quora (but got locked by a moderator pretty quickly so I Googled my way here), and I don't understand how the answerer was able to combine the terms in second last line, it seems like an n disappeared. His answer also seems different to the one in the exercise.

View attachment 33250

Between the different answers, n+(1/2) and 2n+1 seem interchangeable. This looks similar to what I'd do when I'd find a fraction when using the quadratic equation. I don't think I know why that works, only that it does. Is it a similar thing here?

You're missing a "+" sign.

 

[Four Muffins]

You're missing a "+" sign.
View attachment 33254

View attachment 33253

Thank you for your help. Do you know how they get (2n+1)/2 out of n+(1/2)?

 

[Deleted member 4993]

Thank you for your help. Do you know how they get (2n+1)/2 out of n+(1/2)?

n + (1/2 ) = (2n)/2 + (1/2) = (2n + 1)/2

Please go over the calculations, using pencil & paper - do NOT just stare at the screen.

 

[Four Muffins]

n + (1/2 ) = (2n)/2 + (1/2) = (2n + 1)/2

Please go over the calculations, using pencil & paper - do NOT just stare at the screen.

Thank you, Subhotosh. I went over them a bunch of times, but I'm quite new to math, and don't often recognise simple things yet. Sorry about that. I guess I confused this with how factors of quadratic equations that are fractions are treated, like how finding 1/2 becomes 2x-1.