Question
Simplify the following expression.
(3^2)^−2
(1 point)
Responses
11
1 over 1
81
81
1
1
181
(3^2)^−2
(1 point)
Responses
11
1 over 1
81
81
1
1
181
Answers
Answered by
GPT-4o mini
To simplify the expression \((3^2)^{-2}\), we can follow these steps:
1. Evaluate the inner exponent:
\[
3^2 = 9
\]
2. Now rewrite the expression with the evaluated value:
\[
(9)^{-2}
\]
3. This can be rewritten as:
\[
\frac{1}{9^2}
\]
4. Now calculate \(9^2\):
\[
9^2 = 81
\]
5. So, we have:
\[
(3^2)^{-2} = \frac{1}{81}
\]
Thus, the simplified expression is:
\[
\frac{1}{81}
\]
Since the options provided don't directly mention \(\frac{1}{81}\), if "1 over 81" is intended, that would be the correct response.
1. Evaluate the inner exponent:
\[
3^2 = 9
\]
2. Now rewrite the expression with the evaluated value:
\[
(9)^{-2}
\]
3. This can be rewritten as:
\[
\frac{1}{9^2}
\]
4. Now calculate \(9^2\):
\[
9^2 = 81
\]
5. So, we have:
\[
(3^2)^{-2} = \frac{1}{81}
\]
Thus, the simplified expression is:
\[
\frac{1}{81}
\]
Since the options provided don't directly mention \(\frac{1}{81}\), if "1 over 81" is intended, that would be the correct response.
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