To find the rational exponent expression of [tex]\(\sqrt[3]{4n}\)[/tex], we need to recall how to convert a radical expression to an expression with a rational exponent.
The general rule is:
[tex]\[
\sqrt[n]{a} = a^{\frac{1}{n}}
\][/tex]
In this case, we are given [tex]\(\sqrt[3]{4n}\)[/tex]. Following the rule:
[tex]\[
\sqrt[3]{4n} = (4n)^{\frac{1}{3}}
\][/tex]
Thus, the rational exponent expression of [tex]\(\sqrt[3]{4n}\)[/tex] is:
[tex]\[
(4n)^{\frac{1}{3}}
\][/tex]
Therefore, the correct answer is:
[tex]\[
(4n)^{\frac{1}{3}}
\][/tex]
