​$$\text{Find the value of } \left[ \left(\frac{9}{5}\right)^{-6} \times \left(\frac{5}{9}\right)^{-4} \times \left(\frac{1}{3}\right)^{-2} \right]^{-2}$$​​

Correct option is B

Given:

​$$\left[ \left(\frac{9}{5}\right)^{-6} \times \left(\frac{5}{9}\right)^{-4} \times \left(\frac{1}{3}\right)^{-2} \right]^{-2}$$

Formula Used:

a^-n = $$\left(\frac 1a\right)^n$$ 

Solution:

​$$\left[ \left(\frac{9}{5}\right)^{-6} \times \left(\frac95\right)^{4} \times \left(\frac{1}{3}\right)^{-2} \right]^{-2}$$

=$$\left[ \left(\frac{9}{5}\right)^{-6+4} \times \left(\frac{1}{3}\right)^{-2} \right]^{-2}$$

=$$\left[ \left(\frac{9}{5}\right)^{-2} \times \left(\frac{1}{3}\right)^{-2} \right]^{-2}$$

= $$\left[ \left(\frac{9}{5}\times\frac{1}{3}\right)^{-2} \right]^{-2}$$

=$$\left[ \left(\frac{3}{5}\right)^{-2} \right]^{-2}$$ 

=$$\left( \frac35 \right) ^{ -2 \times -2}$$ = $$\left( \frac{3}{5}\right)^4$$​