\[{\text{Evaluate }}{\left( {\frac{1}{4}} \right)^{{{\left( {\frac{1}{4}} \right)}^{{{\left( {\frac{1}{4}} \right)}^{...}}}}}}{\text{ (infinite power tower)}}{\text{.}}\]
\[{\text{If }}N = {\left( {\frac{1}{4}} \right)^{{{\left( {\frac{1}{4}} \right)}^{{{\left( {\frac{1}{4}} \right)}^{...}}}}}}{\text{ then }}{\left( {\frac{1}{4}} \right)^N} = N.{\text{ This equation has one root }}N = \frac{1}{2}.\]
\[\frac{1}{2}\]
