To find the value of \( (23)^{-4} \), we can use the property of negative exponents. The rule states that \( a^{-n} = \frac{1}{a^n} \).
So,
\[ (23)^{-4} = \frac{1}{(23)^4} \]
Now, since \( (23)^4 \) is a positive number, \( (23)^{-4} \) will also be positive.
Calculating \( (23)^4 \): \[ (23)^4 = 23 \times 23 \times 23 \times 23 = 529 \times 529 = 279841 \]
Thus,
\[ (23)^{-4} = \frac{1}{279841} \]
Now, among the options given, none of them yield the exact expression of \( (23)^{-4} \). However, if we check for a logical simplification, we do not find a direct relation. Therefore, among the options provided:
- \(-81/16\)
- \(-16/81\)
- \(81/16\)
- \(16/81\)
None of these are correct.
The value of \( (23)^{-4} \) can be simplified to \( \frac{1}{(23)^4} \), which is much smaller than any of the fractions given.
If you are looking for an answer specifically from the choices provided, the best approximated response deriving from a conceptual understanding of negative powers would be \(16/81\) since it's the only positive answer available, but it does not actually equal \( (23)^{-4} \).
So to conclude: The exact value of \( (23)^{-4} \) is \( \frac{1}{279841} \), which is not listed among your options.