How Do You Solve for N in the Equation AN^(β) = AN^(β - 1)T^(1-β)?

[tracedinair]

Homework Statement

Solve for N:

AN^(β) = AN^(β - 1)T^(1-β)

Homework Equations

The Attempt at a Solution

Here's what I got:

AN^(β) = AN^(β - 1)T^(1-β)

AN^(β) = AN^(β)N^(-1)T^(1)T^(-β)

AN^(β) = AN^(β)T / NT^(-β)

NAN^(β) =AN^(β)T / T^(-β)

N = T/T^(-β)

 

[Mark44]

First off, divide both sides by A.
Then divide by the appropriate quantity so that you have N to some power all by itself on one side.

It's a pretty simple problem if you do the steps above.

 

[tracedinair]

Alright,

AN^(β) = AN^(β-1)T^(1-β)

N^(β) = N^(β)N^(-1)TT^(-β)

1 = N^(-1)TT^(-β)

N = TT^(-β)

Still getting the same thing.

 

[Mark44]

Alright,

AN^(β) = AN^(β-1)T^(1-β)

N^(β) = N^(β)N^(-1)TT^(-β)

1 = N^(-1)TT^(-β)

N = TT^(-β)

Still getting the same thing.

It's correct but can be written more simply as N = T^{1 - β}

In your first post, you have a lot of extra steps that you don't need.
AN^β = AN^β-1T^β-1
<==> N^β = N^β-1T^β-1 (divide both sides by A)
<==> N^β / N^β-1 = T^β-1 (divide both sides by N^β-1
<==> N = T^β-1