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

The required 'option C) 144' is correct.

Step-by-step explanation:

We have,

$(x^{\dfrac{1}{8}})(x^{\dfrac{3}{8}})=12$

To find, the possible value of x = ?

∴ $(x^{\dfrac{1}{8}})(x^{\dfrac{3}{8}})=12$

⇒ $x^{\dfrac{1}{8}+\dfrac{3}{8}}=12$

Using the exponential identity,

$a^{m} a^{n} =a^{m+n}$

⇒ $x^{\dfrac{1+3}{8}}=12$

⇒ $x^{\dfrac{4}{8}}=12$

⇒ $x^{\dfrac{1}{2}}=12$

Squaring both sides, we get

$(x^{\dfrac{1}{2}})^2=(12)^2$

⇒ $x^{{\dfrac{1}{2}}\times2}=144$

⇒ x = 144

∴ The possible value of x = 144

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

Answer 2

Answer:

144

Step-by-step explanation: