# How would I simplifiy this fraction with exponents?

How would I simplify this:

$$\frac{\eta^{k-2}}{\eta_c^k}$$

so that $$\eta_c$$ can also be raised to the power of $$k-2$$?

Would there be an $$\eta_c^2$$ on the top or bottom?

You could simplify it as:

$$\left(\frac{\eta}{\eta_c} \right)^{k-2}\cdot\frac{1}{\eta_c^2}$$

In other words, it would go at the bottom.

It appears that $$\eta_c^2$$ is going to be on the bottom. Given your problem statement, the solution is baby-simple:

$$\frac{\eta^{k-2}}{\eta_c^k}=\frac{\eta^{k-2}}{\eta_c^{k-2+2}}=\frac{\eta^{k-2}}{\eta_c^{k-2}\cdot\eta_c^2}$$

If you want to move $$\eta_c^2$$ to the top, here are the steps to do that:

$$\frac{\eta^{k-2}}{\eta_c^{k-2}\cdot\eta_c^2}=\frac{\eta^{k-2}}{\eta_c^{k-2}}\cdot\frac{1}{\eta_c^2}=\frac{\eta^{k-2}}{\eta_c^{k-2}}\cdot\frac{1}{\eta_c^{-(-2)}}=\frac{\eta^{k-2}}{\eta_c^{k-2}}\cdot\eta_c^{-2}=\frac{\eta^{k-2}\cdot\eta_c^{-2}}{\eta_c^{k-2}}$$