Evaluate (25)4 .(1 point) Responses 16/625 Start Fraction 16 over 625 End Fraction 8/625 Start Fraction 8 over 625 End Fraction 8/20 Start Fraction 8 over 20 End Fraction 16/20

1 answer

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.