To find which option is equivalent to \( 6^{-2} \), we can use the property of exponents that states \( a^{-n} = \frac{1}{a^n} \).
Thus, we can rewrite \( 6^{-2} \) as:
\[ 6^{-2} = \frac{1}{6^2} \]
Now, calculating \( 6^2 \):
\[ 6^2 = 36 \]
So,
\[ 6^{-2} = \frac{1}{36} \]
Now, let's check the provided options to see if any of them match \( \frac{1}{36} \):
- \( 36 \) → Not equivalent
- \( \frac{1}{2^6} \) → This is \( \frac{1}{64} \), not equivalent
- \( \frac{1}{6^{-2}} \) → This is equivalent to \( 6^2 = 36 \), not equivalent
- \( 136 \) → Not equivalent
None of the options seem to directly state \( \frac{1}{36} \). However, if one of the options actually intends to refer to \( \frac{1}{6^2} \), then that would be the correct answer, but it should be correctly written as \( \frac{1}{36} \).
It looks like none of the provided responses accurately represent \( 6^{-2} \). If you check the options again, make sure that the expression is clearly \( \frac{1}{36} \) or \( \frac{1}{6^2} \).
1 answer