​$$\text {If }x = \left( \frac{3}{2} \right)^2 \times \left( \frac{2}{3} \right)^{-4}$$ then find the value of $$x^{-2}$$​​

Correct option is C

​Solution:

$$x = \left( \frac{3}{2} \right)^2 \times \left( \frac{2}{3} \right)^{-4}\\x^{-2} = \left( \left( \frac{3}{2} \right)^2 \times \left( \frac{2}{3} \right)^{-4} \right)^{-2}\\x^{-2} = \left( \frac{2}{3} \right)^{8} \times \left( \frac{3}{2} \right)^{-4}\\x^{-2} = \left( \frac{2^8}{3^8} \right) \times \left( \frac{1}{\left( \frac{3}{2} \right)^4} \right)\\x^{-2} = \frac{2^{8} \cdot 2^4}{3^{8} \cdot 3^4} = \frac{2^{12}}{3^{12}} = \left( \frac{2}{3} \right)^{12}\\$$​​