To solve \(9^{-2}\) using the Property of Negative Integer Exponents, we apply the rule that states \(x^{-n} = \frac{1}{x^n}\).
So, for \(9^{-2}\):
\[ 9^{-2} = \frac{1}{9^2} \]
Now, we calculate \(9^2\):
\[ 9^2 = 81 \]
Therefore:
\[ 9^{-2} = \frac{1}{81} \]
Among the provided options, the correct answer is:
the fraction with numerator 1 and denominator 9 to the negative 2 power.
However, this is a bit ambiguous, as it does not perfectly align with our conclusion, which is \(\frac{1}{81}\). If "the fraction with numerator 1 and denominator 9 to the negative 2 power" is intended to refer to its evaluation, it would have to mean the evaluation leads to \(\frac{1}{81}\).
To summarize, the correct simplified answer to \(9^{-2}\) is \(\frac{1}{81}\).
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