To simplify \(6^{-3}\) using the negative integer rule of exponents, we apply the rule that states \(a^{-n} = \frac{1}{a^n}\).
Thus,
\[ 6^{-3} = \frac{1}{6^3} \]
Now, we can leave our answer in exponential form:
\[ 6^{-3} = \frac{1}{6^3} \]
This is the simplified form of \(6^{-3}\) in terms of exponential form.