Patel Perkins
06/12/2024 · Senior High School
Which of the following is equivalent to \( 6^{-2} \) ? (1 point) \( \frac{1}{6^{2}} \) 36 \( \frac{1}{36} \) \( \frac{1}{2^{6}} \)
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Tutor-Verified Answer
Step-by-step Solution
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 property:
\[
6^{-2} = \frac{1}{6^2}
\]
Now, we can calculate \( 6^2 \):
\[
6^2 = 36
\]
Thus, we have:
\[
6^{-2} = \frac{1}{36}
\]
Now, let's compare this with the options provided:
1. \( \frac{1}{6^{2}} \) (which is \( \frac{1}{36} \))
2. 36
3. \( \frac{1}{36} \)
4. \( \frac{1}{2^{6}} \) (which is \( \frac{1}{64} \))
The correct equivalent expression for \( 6^{-2} \) is:
\[
\frac{1}{36}
\]
So, the answer is \( \frac{1}{36} \).
Quick Answer
The equivalent expression for \( 6^{-2} \) is \( \frac{1}{36} \).
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