To evaluate \( (25)^{-4} \), we use the property of exponents that states \( a^{-n} = \frac{1}{a^n} \). Therefore, we can rewrite:
\[ (25)^{-4} = \frac{1}{(25)^4} \]
Next, we need to calculate \( (25)^4 \).
Calculating \( 25^4 \):
\[ 25^4 = (25^2)^2 = 625^2 \]
Now, we need to find \( 625^2 \):
\[ 625^2 = 625 \times 625 \]
Calculating that, we use the fact that \( 625 = 25 \times 25 \) so:
\[ 625^2 = (25 \times 25)(25 \times 25) = 25^4 = 390625 \]
So, \( 25^4 = 390625 \), then:
\[ (25)^{-4} = \frac{1}{390625} \]
Now we find the values from the given options:
- \( \frac{16}{625} \)
- \( \frac{8}{625} \)
- \( \frac{8}{20} \)
- \( \frac{16}{20} \)
Since \( 390625 = 625 \times 625 \), this shows that \( \frac{1}{390625} \) is less than \( \frac{1}{625} \), and the closest fractions seem much larger than \( 1/390625 \).
None of them provide the exact answer of \( (25)^{-4} \).
To conclude, since \( (25)^{-4} = \frac{1}{390625} \) is not represented in the options given, none of the options are the correct answer.