To evaluate \( (23)^{-4} \), we start by rewriting 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 step-by-step:
- \( 23 \times 23 = 529 \)
- \( 529 \times 23 = 12167 \) (because \( 529 \times 20 + 529 \times 3 = 10580 + 1587 = 12167 \))
- \( 12167 \times 23 = 279841 \) (calculate as \( 12167 \times 20 + 12167 \times 3 = 243340 + 3651 = 279841 \))
So, \( (23)^4 = 279841 \).
Now, substituting back into the expression for \( (23)^{-4} \):
\[ (23)^{-4} = \frac{1}{279841} \]
To express that fraction in terms of the original responses, we leave it as a fraction:
The value of \( (23)^{-4} \) does not match any of the provided options explicitly, which appear to use simpler fractions. A more appropriate answer may be:
- If calculated correctly as \( 279841 \), and in terms of negative fractions, the options that would make sense are evaluated incorrectly.
The fraction we derive is positive, but could be formatted in terms of rate of conversion, leading us to not select from the choices provided as they display the wrong calculations from the base exponent choice.
So we summarize, moving away from the choices, \( \frac{1}{279841} \), and the choices don't reflect the accurate fraction clearly as first elucidate \( (23)^{-4} = 0.0000358 \), implying a misalignment on factorization values. Thus, verifying offers no fitting and the responses do not align mathematically, ensuring no clear answer reflecting appropriate values is exhibited in provided selections.
Thus the correct approximate derived by calculation sureties:
At clearly \( (23)^{-4} \), we ascertain none denote accurately, and thus should opt out as closely matching to existing formulation.