Hey 22upon7.

You have K^(alpha-1) = (r/alpha*A)*N^(alpha-1) Now taking everything to the power (1/(alpha-1) gives

(K^(alpha-1))^(1/(alpha-1)) = K

= [(r/alpha*A)*N^(alpha-1)]^(1/alpha-1)

= N * (r/alpha*A)^(1/(alpha-1))

= (1/(r/alpha*A))^(1/(1-alpha)) * N since a^(-x) = (1/a)^x and x = alpha - 1 in this case.

= (A*alpha/r)^(1/(1-alpha)) * N