Sure, let's evaluate the function [tex]\( f(x) = 5^{2x} \)[/tex] at the given points one by one.
### Step 1: Evaluating [tex]\( f(-1) \)[/tex]
For [tex]\( x = -1 \)[/tex]:
[tex]\[ f(-1) = 5^{2 \cdot (-1)} = 5^{-2} \][/tex]
By the rules of exponents, [tex]\( 5^{-2} \)[/tex] is equivalent to [tex]\( \frac{1}{5^2} \)[/tex]:
[tex]\[ f(-1) = \frac{1}{25} \][/tex]
### Step 2: Evaluating [tex]\( f(0) \)[/tex]
For [tex]\( x = 0 \)[/tex]:
[tex]\[ f(0) = 5^{2 \cdot 0} = 5^0 \][/tex]
Any non-zero number raised to the power of 0 is 1:
[tex]\[ f(0) = 1 \][/tex]
### Step 3: Evaluating [tex]\( f(2) \)[/tex]
For [tex]\( x = 2 \)[/tex]:
[tex]\[ f(2) = 5^{2 \cdot 2} = 5^4 \][/tex]
Calculating [tex]\( 5^4 \)[/tex]:
[tex]\[ 5^4 = 625 \][/tex]
### Conclusion
After evaluating the function at the given points, we have:
- [tex]\( f(-1) = \frac{1}{25} \)[/tex]
- [tex]\( f(0) = 1 \)[/tex]
- [tex]\( f(2) = 625 \)[/tex]
Thus, the correct evaluation gives us:
[tex]\[ f(-1) = \frac{1}{25}, \; f(0) = 1, \; f(2) = 625 \][/tex]
Therefore, the correct choice is:
[tex]\[ \boxed{\frac{1}{25}, \; 1, \; 625} \][/tex]
