Solve for N in this equation: A*N^(β) = (A*N^(β)*T)/N*T^(β))
I tried to work it out and got:
N = T/T^(β)
The solution seems to be correct. It's a pretty straightforward exercise since there are only divisions and multiplications.
You could also write $\displaystyle N=\frac{T}{T^\beta}=T^{1-\beta}$