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The problem asks to evaluate the exponential function \( f(x) = 5^{2x} \) when \( x = -1 \).

Let’s solve it step-by-step:

1. The function is \( f(x) = 5^{2x} \).
2. Plug in \( x = -1 \) into the function:
   \[
   f(-1) = 5^{2(-1)} = 5^{-2}
   \]
3. Simplify \( 5^{-2} \). The negative exponent means the reciprocal:
   \[
   f(-1) = \frac{1}{5^2} = \frac{1}{25}
   \]

So, the correct answer is \( \frac{1}{25} \), which matches the option you selected.

Would you like further details or have any other questions?

Here are 5 related questions you could explore:
1. What is the general rule for simplifying negative exponents?
2. How would the function behave if \( x = 0 \)?
3. What is the value of \( f(x) \) when \( x = 1 \)?
4. How do exponential functions compare to linear functions?
5. What happens when the base of an exponential function is less than 1?

**Tip**: To evaluate exponential functions with negative exponents, always remember that \( a^{-n} = \frac{1}{a^n} \).

Evaluate the exponential function f(x) = 5^{2x} when x = -1.

Learn how to evaluate the exponential function f(x) = 5^{2x} when x = -1. This problem covers key mathematical concepts such as negative exponents and exponential functions. Suitable for students in Grades 8-10.

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