Which of the following is equivalent to 6^-2

Question

1/2^6
1/6^-2
1/36
36

Answer 1

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

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

Calculating \( 6^2 \):

\[ 6^2 = 36 \]

Thus, we have:

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

Now, let's evaluate the options given:

1. \( \frac{1}{2^6} \)
2. \( \frac{1}{6^{-2}} \) (which is actually \( 6^2 \))
3. \( \frac{1}{36} \) (This matches our result)
4. \( 36 \)

The only expression that is equivalent to \( 6^{-2} \) is:

\[ \frac{1}{36} \]

So the correct answer is \( \frac{1}{36} \).