To find [tex]\(\sqrt[8]{6}\)[/tex] in exponential form, you need to understand the concept of roots in the context of exponents. The notation [tex]\(\sqrt[n]{x}\)[/tex] means the [tex]\(n\)[/tex]th root of [tex]\(x\)[/tex], which in terms of exponents is written as [tex]\(x^{\frac{1}{n}}\)[/tex].
So, [tex]\(\sqrt[8]{6}\)[/tex] means the 8th root of 6. Following our rule of converting roots to exponents:
[tex]\[
\sqrt[8]{6} = 6^{\frac{1}{8}}
\][/tex]
Thus, [tex]\(\sqrt[8]{6}\)[/tex] in exponential form is [tex]\(6^{\frac{1}{8}}\)[/tex].
Therefore, the correct choice among the given options is:
[tex]\(6^{\frac{1}{8}}\)[/tex]
