To evaluate \( 6^{-2} \), we can use the properties of negative exponents. Recall that \( a^{-n} = \frac{1}{a^n} \). Therefore,
\[ 6^{-2} = \frac{1}{6^2} \]
Now, calculating \( 6^2 \) gives us \( 6 \times 6 = 36 \). Thus, we have:
\[ 6^{-2} = \frac{1}{36} \]
Now let's compare this with the options you provided:
- \( 36 \)
- \( \frac{1}{36} \)
- \( \frac{1}{6^{-2}} \)
- \( \frac{1}{2^6} \)
The equivalent expression to \( 6^{-2} \) is \( \frac{1}{36} \).
So, the correct answer is \( \frac{1}{36} \).