How Does Dividing Both Sides by (Y/L)α Transform the Production Function?

[albert2008]

Dear People,
This is Production Function and it comes from my economics book. The equation is saying that output per worker (Y/L) is equal to capital per worker (K/L) times the efficiency of labor (E) where alpha is a parameter between zero and one. The chapter is explaining the equation. I don't understand the concept (math) of how the books gets to

(Y/L)1-α= (K/L)α (E)1-α
after it divides both sides by (Y/L)α

Thanks so much and I hope this makes sense

α=alpha (superscript)
1-α=1 minus alpha (superscript)

Y/L=(K/L)α (E)1-α

Rewrite K/L as (K/Y) times (Y/L)

Y/L=(K/Y)α (Y/L)α (E)1-α

Divide both sides by (Y/L)α

(Y/L)1-α= (K/L)α (E)1-α -->Please can someone help me
understand how you get (Y/L)1-α
I don’t understand the logic. Does it have to do with power rule?.

 

[Integral]

You need to provide more information. Just where does this come from? What are you trying to accomplish. We cannot read your mind, you need to provide some background information.

 

[HallsofIvy]

And please explain your notation. You say "Rewrite K/L as (K/Y) times (Y/L)" but then write it as " (K/Y, Y/L)". Do you mean just (K/Y)(Y/L)? Is "1- a" a subscript? I can see no reason for writing 1 if it just multiplying numbers. Finally, what power rule are you talking about? The only power rule I can think of is for differentiating and there is no differentiation here.

 

[Defennder]

As the others have asked you to do, you have to explain what are you trying to show? What is the final answer you want to arrive at?

Following your working, all I can say is that dividing the equation by $$\frac{Y}{L} \alpha$$ gives $$\frac{1}{\alpha} = \frac{K}{Y} E (1-\alpha)$$.

L disappears because it gets divided by both sides. So that's clearly not what you want.