Question

Rezultatul calculului: 2^2^2005 : 2^2^2004 : 2^2^2004 =?

Answer 1

$\begin{aligned}2^{2^{2005}} : 2^{2^{2004}} : 2^{2^{2004}} &= 2^{2^{2005}-2^{2004}}:2^{2^{2004}}\\ &=2^{2^{2005}-2^{2004}-2^{2004}}\\ &= 2^{2^{2005}-2\cdot 2^{2004}}\\ &= 2^{2^{2005}-2^{2004+1}}\\ &= 2^{2^{2005}-2^{2005}}\\ &=2^{0} \\ &=\boxed{1}\end{aligned}$