please help

$\quad \sqrt{11\sqrt{11\sqrt{11\sqrt{11}}}}\\ = \sqrt{11} \cdot 11^{1/4} \cdot 11^{1/8} \cdot 11^{16}\\ = 11^{1/2 + 1/4 + 1/8 + 1/16}\\ = 11^{15/16}$

hint: $\sqrt{11}=11^{1/2}$

What is n?

Hello Guest!

 $11^n=\sqrt{11\sqrt{11\sqrt{11\sqrt{11}}}}= 11^{(\frac{1}{2})^{1+2+3+4}}=11^{ (\frac{1}{2})^{10}}=11^{\frac{1}{1024}}$

 $n=\frac{1}{1024}$

  !

11^1/2  * 11^1/4 * 11^1/8 * 11^1/16   =  11 ^15/16