Chapter R6, Problem 79E

To determine

The value of expression by hand and to approximate the answer to the nearest hundredth when appropriate: $2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} . 2^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$