Question

Assertion: If `x^(2//3) = 4`, then `x = 8`

Reason: `a^(m//n) = root(n)(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:

Assertion:

If `x^(2/3) = 4`, then `x = 8`

To solve:

`x^(2/3) = 4`

⇒ `x = 4^(3/2)`

Now compute:

`4^(3/2) = (sqrt(4))^3 = 2^3 = 8`

So, Assertion is true

Reason:

`a^(m/n) = root(n)(a^m)`

This is correct. That’s the definition of rational exponents.