On comparing the following two numeric expressions, we find that____________.

​$$[(2\frac{7}{9})^{\smash{2\frac{1}{2}}}]^\frac{3}{5}\ and \ [(1\frac{2}{3})^{5}]^\frac{3}{5}$$ 

Correct option is A

Given: ​

$$[(2\frac{7}{9})^{\smash{2\frac{1}{2}}}]^\frac{3}{5}\ and \ [(1\frac{2}{3})^{5}]^\frac{3}{5}$$ 

Solution: ​

Solving the expressions

​$$[(2\frac{7}{9})^{\smash{2\frac{1}{2}}}]^\frac{3}{5} \\ \ \\ = \left(\frac{25}{9}\right)^{\frac52 \times \frac 35}\\ \ \\ = \left(\frac{5}{3}\right)^3 \\ \\ \ \\ = \frac{125}{27}$$ 

second : 

​$$\ [(1\frac{2}{3})^{5}]^\frac{3}{5} \\ \ \\ = \left(\frac{5}{3}\right)^{3} \\ \ \\ = \frac{125}{27}$$ 

Therefore both the expression is equal