General formula of repeated roots. Prove that $$\underbrace{\sqrt{k\sqrt{k\sqrt{k\sqrt{\cdots\sqrt{k}}}}}}_{n\text { times}}=k^{1-1/2^n}$$
How do I derive this formula?

The first $k$ is powered by $\frac{1}{2}$, the second by $\frac{1}{2^2}$ the $n$-therm is then $k^{\frac{1}{2^n}}$ then the expression is equal to:
$$k^{\frac{1}{2^1}}\cdot k^{\frac{1}{2^2}}\cdot \dots  k^{\frac{1}{2^n}}=k^{\sum_{i=1}^n \frac{1}{2^i}}$$
