The expression \( 3\sqrt{5} \) can be rewritten using a rational exponent. The cube root can be expressed as raising to the power of \( \frac{1}{3} \). Therefore, the equivalent expression for \( 3\sqrt{5} \) is:
\[ 5^{\frac{1}{3}} \]
Thus, the rational exponent for \( 3\sqrt{5} \) is \( \frac{1}{3} \).