which of the following is equivalent to 6-^2

Question

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

Answer 1

To evaluate \( 6^{-2} \), we can use the properties of negative exponents. Recall that \( a^{-n} = \frac{1}{a^n} \). Therefore,

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

Now, calculating \( 6^2 \) gives us \( 6 \times 6 = 36 \). Thus, we have:

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

Now let's compare this with the options you provided:

1. \( 36 \)
2. \( \frac{1}{36} \)
3. \( \frac{1}{6^{-2}} \)
4. \( \frac{1}{2^6} \)

The equivalent expression to \( 6^{-2} \) is \( \frac{1}{36} \).

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