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The problem asks to rewrite the expression \((5^{-2})^3\) using positive exponents. Let's solve this step by step.

### Step 1: Apply the power of a power rule
The power of a power rule states that \((a^m)^n = a^{m \cdot n}\).

Here, \(a = 5\), \(m = -2\), and \(n = 3\).

\[
(5^{-2})^3 = 5^{-2 \times 3} = 5^{-6}
\]

### Step 2: Convert to a positive exponent
To convert \(5^{-6}\) to an expression with a positive exponent, use the reciprocal rule: \(a^{-n} = \frac{1}{a^n}\).

\[
5^{-6} = \frac{1}{5^6}
\]

### Final Answer:
The expression \((5^{-2})^3\) in positive exponent form is \(\frac{1}{5^6}\).

Would you like more details on this solution, or do you have any other questions?

### Related Questions:
1. How do you simplify expressions with multiple negative exponents?
2. What is the general rule for multiplying exponents?
3. How do you handle division of exponents with negative powers?
4. Can the laws of exponents be applied to variables as well as numbers?
5. What is the significance of the reciprocal in converting negative exponents?

### Tip:
When simplifying expressions involving exponents, always consider the rules of exponents first before performing any arithmetic operations.

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Learn how to simplify the expression (5^{-2})^3 by rewriting it with a positive exponent. This problem introduces key concepts like the power of a power rule and the reciprocal rule, making it ideal for students in Grades 7-9.

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