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

Question

asked Nov 12, 2021 48.7k views

2 Answers

Lagoru · Answer 1 · 2021-11-16T14:33:42+0000

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.