To simplify the expression \( \sqrt[3]{216} \) using rational exponents, we start by rewriting the expression:
\[ \sqrt[3]{216} = 216^{1/3} \]
Now, if we have \( 216^{1/3} \), we can analyze the exponent part:
- Since \( \sqrt[3]{216} \) means taking the cube root of 216, this is equivalent to raising 216 to the power of \( \frac{1}{3} \).
Therefore, the expression \( \sqrt[3]{216} \) represented as a rational exponent is:
\[ 216^{1/3} \]
The options provided in your question include negative exponents and fractions. Among the options given, the correct equivalent expression for the rational exponent on the expression \( \sqrt[3]{216} \) is:
\[ \frac{1}{3} \]
Thus, the answer is:
Start Fraction 1 over 3 End Fraction.