The value of $${\text{2}}{{\text{7}}^{ - \frac{2}{3}}}$$ lies between = ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{ 2}}{{\text{7}}^{ - \frac{2}{3}}} \cr & = {\left( {{3^3}} \right)^{ - \frac{2}{3}}} \cr & = {3^{\left[ {3 \times \left( { - \frac{2}{3}} \right)} \right]}} \cr & = {3^{ - 2}} \cr & = \frac{1}{{{3^2}}} \cr & = \frac{1}{9} \cr & {\text{Clearly}},\,\,0 < \frac{1}{9} < 1 \cr} $$