To simplify \((c^2)^{-3}\), you can use the property of exponents that states \(a^{-n} = \frac{1}{a^n}\).
So, we have:
\[ (c^2)^{-3} = \frac{1}{(c^2)^3} \]
Now, apply the power of a power property, which says \((a^m)^n = a^{m \cdot n}\):
\[ (c^2)^{3} = c^{2 \cdot 3} = c^{6} \]
Putting it all together, we get:
\[ (c^2)^{-3} = \frac{1}{c^6} \]
Therefore, the simplified version is:
\[ \frac{1}{c^6} \]
Among your answer choices, this corresponds to "1 over c raised to the sixth power."