Step-by-step explanation:
We have,
[tex](x^{\dfrac{1}{8}})(x^{\dfrac{3}{8}})=12[/tex]
To find, the possible value of x = ?
∴ [tex](x^{\dfrac{1}{8}})(x^{\dfrac{3}{8}})=12[/tex]
⇒ [tex]x^{\dfrac{1}{8}+\dfrac{3}{8}}=12[/tex]
Using the exponential identity,
[tex]a^{m} a^{n} =a^{m+n}[/tex]
⇒ [tex]x^{\dfrac{1+3}{8}}=12[/tex]
⇒ [tex]x^{\dfrac{4}{8}}=12[/tex]
⇒ [tex]x^{\dfrac{1}{2}}=12[/tex]
Squaring both sides, we get
[tex](x^{\dfrac{1}{2}})^2=(12)^2[/tex]
⇒ [tex]x^{{\dfrac{1}{2}}\times2}=144[/tex]
⇒ x = 144
∴ The possible value of x = 144
Thus, the required 'option C) 144' is correct.
