To evaluate \( (23)^{-4} \), we can rewrite it using the property of negative exponents:
\[ (23)^{-4} = \frac{1}{(23)^4} \]
Next, we need to calculate \( (23)^4 \):
\[ (23)^4 = 23 \times 23 \times 23 \times 23 \]
Calculating this step by step:
- \( 23 \times 23 = 529 \)
- \( 529 \times 23 = 12167 \)
- \( 12167 \times 23 = 279841 \)
So, \( (23)^4 = 279841 \).
Now, substituting this back into the expression:
\[ (23)^{-4} = \frac{1}{279841} \]
To see if any of the given options match this result:
The options are:
- \( 81/16 \)
- \( 16/81 \)
- \( -1681 \)
- \( -81/16 \)
None of those directly correspond to \( \frac{1}{279841} \).
However, if we consider the fraction \( \frac{1}{(23)^4} \), it is straightforward that the appropriate form would not be among the choices unless further simplifications or relations can be made. Given these are the options and none fit, we would need to confirm:
Since \( 23^4 \) cannot simplify to any of the provided forms, none of these options represent \( (23)^{-4} \).
Thus, the value of \( (23)^{-4} \) is indeed \( \frac{1}{279841} \), but it doesn't align with any of the provided choices.