# Fractional Exponents Microeconomics

I need to find $$X_a$$ using this equation. I am having trouble working out how they got this answer. The question is $$Y=X_a^{1/3} \left(\frac{w_a}{w_2} X_a \right)^{1/3}$$ The answer works out to be $$X_a=Y^{3/2}\left(\frac{w_2}{w_a} \right)^{1/2}$$

Click the link below to see my teachers working out. (If that helps) Here is my teachers working out...

• What have you tried? The first phase would be to open the parentheses so that you can isolate $X_a$ (I mean: so that there is only one mention of $X_a$ in the right-hand-side of the equation) – Matti P. Apr 16 at 9:45
• Cube both sides first – Claude Leibovici Apr 16 at 9:46

$$Y=X_a^{1/3}\left( \frac{w_a}{w_2}X_a\right)^{1/3}$$
$$Y^3=X_a\left( \frac{w_a}{w_2}X_a\right)=\frac{w_a}{w_2}(X_a)^2$$
$$(X_a)^2=Y^3\cdot \frac{w_2}{w_a}$$
$$X_a=Y^{3/2}\cdot \left(\frac{w_2}{w_a}\right)^{1/2}$$