Which of the following is equivalent to 6^−2?

Question

options:

1 over 6^−2

1 over 2^6

36

1 over 36

Answer 1

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

Thus,

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

Now, let's consider the options:

1. 1 over 6^−2: This is equivalent to \( 6^2 \), not 6^−2.
2. 1 over 2^6: This is irrelevant as it doesn't relate directly to our simplification of \( 6^{-2} \).
3. 36: This is not equivalent to \( 6^{-2} \) since \( 6^{-2} \) equals \( \frac{1}{36} \).
4. 1 over 36: This is exactly \( 6^{-2} \).

Thus, the correct answer is:

1 over 36.