Question

Which of the following is equivalent to six to the negative second power
1. one half to the sixth power
2. thirty six
3. one half to the sixth power
4. one thirtsixths

Answer 1

To evaluate \( 6^{-2} \), we can use the property of negative exponents:

\[
a^{-n} = \frac{1}{a^n}
\]

So,

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

Calculating \( 6^2 \):

\[
6^2 = 36
\]

Thus,

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

Now, let's look at your options:

1. \( \frac{1}{2^6} \) is not equal to \( \frac{1}{36} \).
2. \( 36 \) is not equal to \( \frac{1}{36} \).
3. \( \frac{1}{2^6} \) is the same option as the first one.
4. \( \frac{1}{36} \) is indeed equal to \( 6^{-2} \).

Therefore, the equivalent expression is:

**4. one thirty-sixth**.