fraction rased to a power of log base 2

Question

The below expression simplifies to $\frac{y}{n}$, $$ \left(\dfrac{1}{2} \right)^{\log_2\left(\frac{1}{y/n}\right)} $$

I have tried to change bases but haven't figured out how to come up with the solution $y/n$.

Thanks in advance.

Answer 1

let $y/n = x$ $$(2^{-1})^{\log_2 x^{-1}} =2^{\log_2 x}=x=\frac{y}{n}$$