we have
[tex](x^{\frac{1}{8}})(x^{\frac{3}{8}})=12[/tex]
we know that
[tex](x^{\frac{1}{8}})(x^{\frac{3}{8}})=12\\ \\x^{(\frac{1}{8}+{\frac{3}{8}})}=12\\ \\x^{\frac{4}{8}}=12\\ \\x^{\frac{1}{2}}=12[/tex]
Square both sides
[tex]x^{(\frac{1}{2})^{2}} =12^{2}[/tex]
[tex]x^{\frac{2}{2}}=12^{2} \\\\x=144[/tex]
therefore
the answer is the option C
[tex]144[/tex]
The fraction power of exponent should be add using power rule of exponents.
The Possible value of the [tex]x[/tex] is 144 for the given expression. The option C is the correct option.
Power rule of exponents states that, when the two number with same base are multiplied then the exponents of both the numbers added.
Given information-
The expression given in the problem is,
[tex](x^\dfrac{1}{8}}) (x^\dfrac{3}{8}} )=12[/tex]
As in the above equation the base [tex]x[/tex] is same for both number. Thus the fraction power of exponent should be add using power rule of exponents.
Therefore,
[tex](x^\dfrac{1}{8}}^+^\dfrac{3}{8}) } )=12\\x^\dfrac{4}{8} }=12\\x^\dfrac{1}{2}} =12\\\sqrt{x} =12[/tex]
Square both sides,
[tex]x=12^2\\x=144[/tex]
Hence the value of the [tex]x[/tex] is 144 for the given expression. The option C is the correct option.
Learn more about the power rule of exponents here;
https://brainly.com/question/819893
