Assertion (A): If we divide 3^-2 by 3⁴, we get 9³.

Reason (R): $\Big(\dfrac{x}{y}\Big)^{-m} = \dfrac{y^{-m}}{x^{-m}}$

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Solving,

$\Rightarrow \dfrac{3^{-2}}{3^4} \\[1em] \Rightarrow 3^{-2 - 4} \\[1em] \Rightarrow 3^{-6} \\[1em] \Rightarrow (3^2)^{-3} \\[1em] \Rightarrow 9^{-3}.$

∴ Assertion (A) is false.

According to reason (R) :

$\Big(\dfrac{x}{y}\Big)^{-m} = \dfrac{y^{-m}}{x^{-m}}$

Solving L.H.S,

$\Rightarrow \Big(\dfrac{x}{y}\Big)^{-m} \\[1em] \Rightarrow \Big(\dfrac{y}{x}\Big)^{m} \\[1em] \Rightarrow \Big(\dfrac{y^m}{x^m}\Big) \\[1em]$

Since, L.H.S ≠ R.H.S

∴ Reason (R) is false.

Both A and R are false.

Hence, option 4 is the correct option.