Question

Assertion: `(81/49)^((-3)/2) = (7/9)^3`

Reason: `(a/b)^-m = (b/a)^m`

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

Let’s analyze both the Assertion and Reason:

Assertion:

`(81/49)^(-3/2) = (7/9)^3`

First, simplify the left-hand side:

`(81/49)^(-3/2) = (49/81)^(3/2)`   ...(By using (a/b)^–m = (b/a)^m)

Now compute `(49/81)^(3/2)`:

• `sqrt(49/81) = 7/9`
• Then raise it to the power 3: `(7/9)^3`

So, `(81/49)^(-3/2) = (7/9)^3`

Assertion is true

Reason:

`(a/b)^-m = (b/a)^m`

This is a standard law of exponents and also true.