To express the cube root of 216 using rational exponents, we can use the property that states:
\[ \sqrt[n]{a} = a^{\frac{1}{n}} \]
In our case, we need to find the cube root of 216, which is expressed as:
\[ \sqrt[3]{216} = 216^{\frac{1}{3}} \]
Thus, the rational exponent on an expression equivalent to the cube root of 216 is:
\[ \frac{1}{3} \]
So the answer is \( \frac{1}{3} \).