To find the rational exponent equivalent to \( \sqrt[3]{216} \), we can rewrite it using the properties of exponents.
The cube root can be expressed as an exponent of \( \frac{1}{3} \): \[ \sqrt[3]{216} = 216^{\frac{1}{3}} \]
Now, to relate \( 216^{\frac{1}{3}} \) to the expression \( 216^{-\frac{1}{3}} \), we note that in the original question you have \( \sqrt[3]{216}^3 \) (if that's what it means by 216 raised to the power of "negative 3"). But if we consider only \( 216^{\frac{1}{3}} \), it remains as above:
To summarize, the rational exponent on an expression equivalent to \( \sqrt[3]{216} \) is: \[ \frac{1}{3} \]
Thus, the correct response is: Start Fraction 1 over 3 End Fraction