Let's determine the rational exponent expression for the sixth root of [tex]\( f \)[/tex].
Given the notation [tex]\(\sqrt[6]{f}\)[/tex], we need to convert the radical form into an expression with a rational exponent.
In general, the [tex]\( n \)[/tex]-th root of a number [tex]\( a \)[/tex] can be expressed with a rational exponent as:
[tex]\[
\sqrt[n]{a} = a^{\frac{1}{n}}
\][/tex]
For this specific problem, we have [tex]\( n = 6 \)[/tex] and [tex]\( a = f \)[/tex]. Substituting these values into the formula, we get:
[tex]\[
\sqrt[6]{f} = f^{\frac{1}{6}}
\][/tex]
Thus, the rational exponent expression for [tex]\(\sqrt[6]{f}\)[/tex] is:
[tex]\[
f^{\frac{1}{6}}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{f^{\frac{1}{6}}}
\][/tex]
