To determine the rational exponent expression of the fourth root of [tex]\( f \)[/tex], we start by rewriting the expression [tex]\(\sqrt[4]{f}\)[/tex] in terms of exponents.
The notation [tex]\(\sqrt[4]{f}\)[/tex] represents the fourth root of [tex]\(f\)[/tex], and a general property of exponents is that the [tex]\(n\)[/tex]-th root of a number [tex]\(a\)[/tex] can be expressed as [tex]\( a^{\frac{1}{n}} \)[/tex].
In this case:
[tex]\[
\sqrt[4]{f} = f^{\frac{1}{4}}
\][/tex]
Thus, the rational exponent expression of the fourth root of [tex]\( f \)[/tex] is:
[tex]\[
f^{\frac{1}{4}}
\][/tex]
So, the correct choice is [tex]\( f^{\frac{1}{4}} \)[/tex].
