Question

(i) `(64)^(-3//2) = 512`

(ii) `5^-1 xx 3^0 = 1/5`

विकल्प

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (ii)

Explanation:

Let’s verify each given statement:

(i) `(64)^(-3//2) = 512`

64 = 4³ 

Then `(64)^(-3//2) = (4^3)^(-3//2)`

`(64)^(-3//2) = 4^(3 xx (-3//2)`

`(64)^(-3//2) = 4^(-9//2)`

`4^(9//2) = (4^(1//2))^9`

4^9/2 = (2)⁹

4^9/2 = 512

Hence, `4^(-9//2) = 1/4^(9//2) = 1/512`, which is not equal to 512. 

So statement (i) is false.

(ii) `5^-1 xx 3^0 = 1/5`

`5^-1 = 1/5`

3⁰ = 1

Therefore,

`5^-1 xx 3^0 = 1/5 xx 1`

`5^-1 xx 3^0 = 1/5`

So statement (ii) is true.

Thus, only statement (ii) is valid.