Insert variable into function and solve for another variable I have the following production function:

$$y=x_1^{0.4}\cdot x_2^{0.4}$$

and I know that $x_1 = \dfrac{x_2}2$.

I need to plug $x_1$ into the production function and solve it for $x_2$.

I've tried it this way:

$$y = \left(\dfrac{x_2}2\right)^{0.4}\cdot x_2^{0.4}$$

Unfortunately, I'm not sure how I can solve this for $x_2$.

I would be grateful for any help!
Assuming everything is positive

$$y = \left(\dfrac{x_2}2\right)^{0.4}\cdot x_2^{0.4}$$

$$y = \left(\dfrac{x_2^2}2\right)^{0.4}$$

$$y^{2.5} = \dfrac{x_2^2}2$$

$$2 y^{2.5} = x_2^2 $$

$$\sqrt{2} y^{1.25} = x_2 $$
Hint: I would simplify your expression by replacing an awkward term like $x_1^{0.4}$ by the term $\sqrt[5]{x_1^2}$. Now you can proceed by using more algebraic techniques.