To evaluate \( 6^{-2} \), we can use the property of exponents that states \( a^{-n} = \frac{1}{a^n} \). Thus:
\[ 6^{-2} = \frac{1}{6^2} = \frac{1}{36} \]
Now let's analyze the provided options to see which one is equivalent to \( 6^{-2} \):
- 36: This is not equivalent; \( 6^{-2} = \frac{1}{36} \) is not equal to \( 36 \).
- \(\frac{1}{2^6}\): This is equal to \(\frac{1}{64}\), which is not equivalent to \( \frac{1}{36} \).
- \(\frac{1}{6^{-2}}\): This can be rewritten using the property of exponents. \( 6^{-2} \) is \( \frac{1}{36} \), so \( \frac{1}{6^{-2}} = 6^2 = 36 \). Not equivalent.
- 136: This is not equivalent; \( 6^{-2} = \frac{1}{36} \) is clearly not equal to 136.
It appears that none of the options listed are equivalent to \( 6^{-2} \). However, our calculated value of \( 6^{-2} \) is \( \frac{1}{36} \), which does not match provided responses either.
Please clarify the options if there are any mistakes or consider that the accurate equivalent of \( 6^{-2} \) is indeed \( \frac{1}{36} \).