# Homework Help: Solve for the variable?

1. Feb 16, 2010

### tracedinair

1. The problem statement, all variables and given/known data

Solve for N:

AN^(β) = AN^(β - 1)T^(1-β)

2. Relevant equations

3. 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)

2. Feb 17, 2010

### Staff: Mentor

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.

3. Feb 17, 2010

### 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.

4. Feb 17, 2010

### Staff: Mentor

It's correct but can be written more simply as N = T1 - β

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