$\Big(\dfrac{25}{9}\Big)^{-\dfrac{3}{2}}$ is equal to :

1. $\Big(\dfrac{5}{3}\Big)^3$

2. $\Big(\dfrac{5}{3}\Big)^2$

3. $\dfrac{27}{125}$

4. $\Big(\dfrac{3}{5}\Big)^{-2}$

Simplifying the expression :

$\Rightarrow \Big(\dfrac{25}{9}\Big)^{-\dfrac{3}{2}} = \Big[\Big(\dfrac{5}{3}\Big)^2\Big]^{-\dfrac{3}{2}} \\[1em] = \Big(\dfrac{5}{3}\Big)^{-3} = \Big(\dfrac{3}{5}\Big)^3 \\[1em] = \dfrac{27}{125}.$

Hence, Option 3 is the correct option.