To convert \( 3^{-12} \) using the Negative Exponent Rule, we use the rule that states \( a^{-n} = \frac{1}{a^n} \).
So, applying this rule:
\[ 3^{-12} = \frac{1}{3^{12}} \]
Now, to express \( 3^{12} \) in radical form, we can rewrite it as:
\[ 3^{12} = (3^6)^2 \]
Thus, we can express it in radical form:
\[ 3^{12} = \sqrt{(3^6)^4} = 3^6 \sqrt{3^6} \]
However, using the exponent as a whole, we simply have:
\[ 3^{-12} = \frac{1}{3^{12}} = \frac{1}{(3^6)^2} = \frac{1}{\sqrt{3^{24}}} \]
Thus, the final answer is:
\[ 3^{-12} = \frac{1}{3^{12}} = \frac{1}{\sqrt{(3^6)^4}} = \frac{1}{\sqrt{3^{24}}} \]
So in simplest radical form:
\[ 3^{-12} = \frac{1}{3^{12}} \]
This can simply be written as:
\[ = \frac{1}{\sqrt{3^{24}}} \]
Conclusively:
\[ 3^{-12} = \frac{1}{3^{12}} \]