Question

Which of the following is equivalent to 6^−2 36 1/6^-2 1/36 1/2^6

Answer 1

To simplify \( 6^{-2} \), we can use the property of exponents that states \( a^{-n} = \frac{1}{a^n} \). Therefore:

\[ 6^{-2} = \frac{1}{6^2} \]

Calculating \( 6^2 \):

\[ 6^2 = 36 \]

Thus, we have:

\[ 6^{-2} = \frac{1}{36} \]

Now, we can check the provided options:

1. \( 36 \) - Not equivalent.
2. \( \frac{1}{6^{-2}} \) - This is equivalent to \( 6^2 \), which is \( 36 \).
3. \( \frac{1}{36} \) - Equivalent to \( 6^{-2} \).
4. \( \frac{1}{2^6} \) - Not equivalent.

The correct answer is:

\(\frac{1}{36}\)