Question

Which of the following is equivalent to 6 raised to the −2 power?(1 point)
Responses

136
Start Fraction 1 over 36 End Fraction

126
Start Fraction 1 over 2 superscript 6 baseline End Fraction

16−2
Start Fraction 1 over 6 superscript negative 2 baseline End Fraction

36

Answer 1

To find the equivalent expression for \( 6^{-2} \), we can use the property of exponents that states \( a^{-n} = \frac{1}{a^n} \).

Applying this to \( 6^{-2} \):

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

Calculating \( 6^2 \):

\[
6^2 = 36
\]

Thus,

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

Now, looking at the options provided:

1. \( \frac{1}{36} \) - This is correct.
2. \( \frac{1}{2^6} \) - This is not equivalent.
3. \( \frac{1}{6^{-2}} \) - This is incorrect since it represents \( 6^2 \), not \( 6^{-2} \).
4. \( 36 \) - This is incorrect as it is the value of \( 6^2 \), not \( 6^{-2} \).

Therefore, the correct answer is:

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