To solve the expression \( (23)^{-4} \), we start by rewriting it in a more manageable form:
\[ (23)^{-4} = \frac{1}{(23)^4} \]
Next, we need to calculate \( (23)^4 \):
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Calculate \( 23^2 \): \[ 23^2 = 529 \]
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Now, square \( 529 \) to get \( 23^4 \): \[ 23^4 = 529^2 \]
Calculating \( 529^2 \): \[ 529^2 = 279841 \]
Now we substitute back into our expression: \[ (23)^{-4} = \frac{1}{(23)^4} = \frac{1}{279841} \]
So the value of \( (23)^{-4} \) is: \[ \frac{1}{279841} \]
Given none of the provided responses matches \( \frac{1}{279841} \), let's analyze the provided options:
- \( -8116 \)
- \( -\frac{81}{16} \)
- \( -\frac{16}{81} \)
- \( \frac{16}{81} \)
- \( \frac{8116}{1} \)
Since we can see that our valid outcome isn't in the answer choices, it seems there was a misunderstanding. If we are to analyze based on exponent multiplication or conversion,
we don't have the correct fractional representation as:
\[ (23)^{-4} \text{ equals none of the listed options.} \]
For \( (23)^{-4} \), we directly arrive at \( \frac{1}{279841}, \) and since this isn't given among the choices, the correct option might not be present.
If re-evaluating accurately leads us against \( \frac{1}{279841} \), kindly verify the options provided or context if \( (23)^{-4} \) is not the intent.