To determine the rational exponent expression of [tex]\(\sqrt[6]{f}\)[/tex], we need to understand the relationship between roots and exponents.
In mathematics, the [tex]\(n\)[/tex]th root of a number or variable can be expressed as a power with a fractional exponent. Specifically:
[tex]\[
\sqrt[n]{f} = f^{\frac{1}{n}}
\][/tex]
In our case, we are looking for the 6th root of [tex]\(f\)[/tex]. This means we will apply the rule using [tex]\(n = 6\)[/tex]. Therefore, the 6th root of [tex]\(f\)[/tex] can be written as:
[tex]\[
\sqrt[6]{f} = f^{\frac{1}{6}}
\][/tex]
Among the provided options, the expression that matches [tex]\(f^{\frac{1}{6}}\)[/tex] is exactly [tex]\(f^{\frac{1}{6}}\)[/tex].
Thus, the correct answer is:
[tex]\[
f^{\frac{1}{6}}
\][/tex]
