To find the rational exponent of the expression \( 216^{-\frac{1}{3}} \), we can rewrite the expression using the properties of exponents.
The expression \( 216^{-\frac{1}{3}} \) can be interpreted as:
- The negative exponent indicates that we are taking the reciprocal of the base raised to the positive exponent.
- The fractional exponent indicates the root; specifically, the denominator of the fraction represents the root.
Thus:
\[ 216^{-\frac{1}{3}} = \frac{1}{216^{\frac{1}{3}}} \]
Now, to determine the form of \( 216^{\frac{1}{3}} \):
- The cube root of \( 216 \) is \( 6 \) since \( 6^3 = 216 \).
Therefore:
\[ 216^{-\frac{1}{3}} = \frac{1}{6} \]
From the options given, the equivalent expression with the rational exponent in \( 216^{-1/3} \) is simply:
\(-\frac{1}{3}\)
So the rational exponent on an expression equivalent to \( 216^{-\frac{1}{3}} \) is:
\(-\frac{1}{3}\)
Thus, the answer is:
−1/3