To determine the rational exponent expression of [tex]\(\sqrt[4]{f}\)[/tex], we need to recall the relationship between radical expressions and rational exponents. Specifically, the [tex]\(n\)[/tex]-th root of a number can be expressed as a rational exponent with the number being raised to the power of [tex]\(\frac{1}{n}\)[/tex].
Given that we are looking for the expression of the fourth root of [tex]\(f\)[/tex]:
[tex]\[
\sqrt[4]{f}
\][/tex]
We can convert this radical expression to a rational exponent. The general rule for converting an [tex]\(n\)[/tex]-th root to a rational exponent is:
[tex]\[
\sqrt[n]{x} = x^{\frac{1}{n}}
\][/tex]
Applying this rule to the fourth root of [tex]\(f\)[/tex], we replace [tex]\(n\)[/tex] with 4:
[tex]\[
\sqrt[4]{f} = f^{\frac{1}{4}}
\][/tex]
Among the given options, the expression that matches [tex]\(f^{\frac{1}{4}}\)[/tex] is:
[tex]\[
f^{\frac{1}{4}}
\][/tex]
Thus, the correct answer is:
[tex]\[
1. \; f^{\frac{1}{4}}
\][/tex]
