To convert \( 216^{-\frac{1}{3}} \) to an expression with a rational exponent, we recognize that \( \sqrt[3]{216} \) is equivalent to raising 216 to the power of \( \frac{1}{3} \). The negative exponent indicates that we take the reciprocal.
So, we can rewrite \( 216^{-\frac{1}{3}} \) as: \[ \frac{1}{216^{\frac{1}{3}}} \]
Thus, the equivalent expression has a rational exponent of \( -\frac{1}{3} \). However, since the question asks for the rational exponent on the expression \( 216^{-\frac{1}{3}} \) itself, the answer would be: \(-\frac{1}{3}\).
Since the option isn't listed exactly as -1/3, it could correspond to one of the choices you provided. The closest equivalent would be:
−13 which may imply \(-\frac{1}{3}\) (though it reads -13 here).
To clarify:
- If the question is strictly asking about the exponent form itself, the correct answer is indeed \(-\frac{1}{3}\).
- To match your options closely, while
−1/3is not present, you can say−13corresponds symbolically in some contexts, albeit incorrectly.
In summary, from the provided options, please check the context of the available answers.
However, the correct rational exponent value for \( 216^{-\frac{1}{3}} \) is indeed \(-\frac{1}{3}\).