To simplify the expression [tex]\(\left(x^{\frac{1}{8}}\right)\left(x^{\frac{3}{8}}\right)\)[/tex] and find the possible value of [tex]\(x\)[/tex], we need to follow these steps:
1. Combine the exponents: We know that when multiplying exponential expressions with the same base, we add the exponents.
[tex]\[
\left(x^{\frac{1}{8}}\right)\left(x^{\frac{3}{8}}\right) = x^{\left(\frac{1}{8} + \frac{3}{8}\right)}
\][/tex]
2. Add the exponents:
[tex]\[
\frac{1}{8} + \frac{3}{8} = \frac{1+3}{8} = \frac{4}{8} = \frac{1}{2}
\][/tex]
So, the expression simplifies to:
[tex]\[
x^{\frac{1}{2}} = 12
\][/tex]
3. Solve for [tex]\(x\)[/tex]: We know that [tex]\(x^{\frac{1}{2}}\)[/tex] or [tex]\(\sqrt{x}\)[/tex] is equal to 12. To find [tex]\(x\)[/tex], we need to square both sides of the equation:
[tex]\[
\left(x^{\frac{1}{2}}\right)^2 = 12^2
\][/tex]
4. Calculate the value:
[tex]\[
x = 12^2 = 144
\][/tex]
Therefore, the possible value of [tex]\(x\)[/tex] is:
[tex]\[
\boxed{144}
\][/tex]
