Which of the following is equivalent to 6−2

Question

?(1 point)
Responses

36
36

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

136
Start Fraction 1 over 36 End Fraction

126
Start Fraction 1 over 2 superscript 6 baseline End Fraction
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Answer 1

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

Thus,

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

Now, let's look at the given options:

1. 36
2. \( 16^{-2} \)
3. \( \frac{1}{36} \)
4. \( \frac{1}{2^6} \)

Among these options, the only one that matches \( \frac{1}{36} \) is option 3.

So, the equivalent expression to \( 6^{-2} \) is:

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