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The expression to simplify is \( (5^{-2})^3 \).

To simplify this, apply the **power of a power rule**, which states:
\[
(a^m)^n = a^{m \cdot n}
\]

In this case, we have \( 5^{-2} \) raised to the power of 3:
\[
(5^{-2})^3 = 5^{-2 \cdot 3} = 5^{-6}
\]

Since \( 5^{-6} = \frac{1}{5^6} \), the correct answer is:
\[
\boxed{\frac{1}{5^6}}
\]

Would you like a detailed breakdown or have any questions? Here are five related questions:

1. How do you handle negative exponents in general?
2. What is the rule for multiplying exponents with the same base?
3. Can you convert a negative exponent into a fraction?
4. How would you simplify \( (2^{-3})^4 \)?
5. What happens when a base raised to a negative exponent is squared?

**Tip**: When you encounter a negative exponent, remember that it simply means taking the reciprocal of the base raised to the corresponding positive exponent.

Learn how to simplify the expression (5^(-2))^3 using the power of a power rule and the negative exponent rule. This problem covers key exponentiation concepts, suitable for students in Grades 8-10.

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