Hello

The problem says to insert brackets to make this a true statement

$\displaystyle

\sqrt{2}^{{\sqrt{2}}^{{\sqrt{2}}^{\sqrt{2}}}} =

\sqrt{2}^{{\sqrt{2}}^{\sqrt{2}}}

$

I know that:

$\displaystyle

\sqrt{2}^{\sqrt{2}} = 2^{\frac{\sqrt2}{2}}

$

$\displaystyle

(\sqrt{2}^{\sqrt{2}})^{\sqrt{2}} = 2

$

I'm not sure how to proceed from here, apart from brute force. A hint would be appreciated.