(-2)^-1 ÷ (-2)^-4 is equal to:

1. 8

2. $\dfrac{1}{8}$

3. -8

4. -$\dfrac{1}{8}$

If $\dfrac{a}{b} = \dfrac{2}{3} ÷ \Big(-\dfrac{2}{3}\Big)^0; \text{then} \Big(\dfrac{a}{b}\Big)^{-2}$ is equal to:

1. $\dfrac{4}{9}$

2. $-\dfrac{4}{9}$

3. $\dfrac{9}{4}$

4. $-\dfrac{9}{4}$

(2 + 3)^-1 x (2^-1 + 3^-1) is equal to :

1. 6

2. -6

3. $\dfrac{1}{6}$

4. $-\dfrac{1}{6}$

Statement 1: $\Big(\dfrac{3}{4}\Big)^{-4} \times \Big(\dfrac{3}{4}\Big)^{-5} = \Big(\dfrac{3}{4}\Big)^{3x}$

⇒ x = -1

Statement 2: $\Big(\dfrac{3}{4}\Big)^{-4 - 5} = \Big(\dfrac{3}{4}\Big)^{3x}$

⇒ 3x = -9

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.