The value of 2 7^ - 2/3 lies between = ?

Answer: Option A

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