To express the given radical expression in rational exponent form, let's start by understanding the notation. The expression is given as:
[tex]\[
\sqrt[3]{5xy^2}
\][/tex]
This can be interpreted as raising the entire quantity [tex]\( 5xy^2 \)[/tex] to the power of [tex]\(\frac{1}{3}\)[/tex].
By definition, the radical expression [tex]\(\sqrt[3]{a}\)[/tex] can be written with a rational exponent as [tex]\(a^{\frac{1}{3}}\)[/tex]. Applying this rule to our expression:
[tex]\[
\sqrt[3]{5xy^2} = (5xy^2)^{\frac{1}{3}}
\][/tex]
So the correct expression in rational exponent form is:
[tex]\[
\left(5xy^2\right)^{\frac{1}{3}}
\][/tex]
Thus, the correct answer is:
[tex]\[
\left(5xy^2\right)^{\frac{1}{3}}
\][/tex]
