Question

When simplified, the expression (x Superscript one-eighth Baseline) (x Superscript three-eighths Basleline) is 12. Which is a possible value of x?

6
24
144
256

Answer 1

144

Explanation:

Answer 2

The required 'option C) 144' is correct.

Explanation:

We have,

`(x^{(1)/(8)})(x^{(3)/(8)})=12`

To find, the possible value of x = ?

∴
`(x^{(1)/(8)})(x^{(3)/(8)})=12`

⇒
`x^{(1)/(8)+(3)/(8)}=12`

Using the exponential identity,

`a^(m) a^(n) =a^(m+n)`

⇒
`x^{(1+3)/(8)}=12`

⇒
`x^{(4)/(8)}=12`

⇒
`x^{(1)/(2)}=12`

Squaring both sides, we get

`(x^{(1)/(2)})^2=(12)^2`

⇒
`x^{{(1)/(2)}*2}=144`

⇒ x = 144

∴ The possible value of x = 144

Thus, the required 'option C) 144' is correct.