What $n^{\frac{1}{\log_2n}}$ means?

Question

I was confused with about the $n^{\frac{1}{\log_2n}}$ expression. I am not sure how to make mathematical sense of it - i.e. express it in another way for easier understanding. I tried to plug in some numbers like $4$ and $8$. I got the answer $2$ in both cases. Is it what this expression means? $2$?

Answer 1

Let:$$n^{\frac{1}{\log_2n}}=x$$Then take logs of both sides to get:$$\log_2(n^{\frac{1}{\log_2n}})=\log_2(x)$$$$\require{cancel}\therefore\frac{1}{\cancel{\log_2n}}\cancel{\log_2(n)}=\log_2(x)$$$$\therefore 1=\log_2x$$$$\therefore x=2$$

Answer 2

$$n^{\frac{1}{\log_2{n}}}=(2^{\log_2{n}})^{\frac{1}{\log_2{n}}}=2^{\log_2{n}\cdot\frac{1}{\log_2{n}}}=2^1=2$$

Answer 3

$$n^\dfrac1{\log_2n}=n^{\log_n2}=2$$