Assertion (A): Value of $\Big(\dfrac{8}{162}\Big)^{-1.5}$ is $\Big(\dfrac{729}{8}\Big)$.

Reason (R): x^m × yⁿ = (xy)^{m + n}

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,

$\Rightarrow \Big(\dfrac{8}{162}\Big)^{-1.5} \\[1em] \Rightarrow \Big(\dfrac{2^3}{2 \times 9^2}\Big)^{-1.5} \\[1em] \Rightarrow \Big(\dfrac{2^{3 - 1}}{9^2}\Big)^{-1.5} \\[1em] \Rightarrow \Big(\dfrac{2^2}{9^2}\Big)^{-1.5} \\[1em] \Rightarrow \Big[\Big(\dfrac{2}{9}\Big)^2\Big]^{-\dfrac{3}{2}} \\[1em] \Rightarrow \Big(\dfrac{2}{9}\Big)^{2 \times -\dfrac{3}{2}} \\[1em] \Rightarrow \Big(\dfrac{2}{9}\Big)^{-3} \\[1em] \Rightarrow \Big(\dfrac{9}{2}\Big)^{3} \\[1em] \Rightarrow \dfrac{729}{8}.$

Assertion (A) is true.

x^m × yⁿ = (xy)^{m + n} is not correct in general.

Correct identity:

⇒ x^m × y^m = (xy)^m

Or

⇒ x^m × xⁿ = x^m+n

Reason (R) is false.

A is true, R is false

Hence, option 1 is the correct option.