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The given expression is:

\[
5^2 \cdot 5^{-3} \cdot 5^{-1}
\]

To simplify, we use the property of exponents that states:

\[
a^m \cdot a^n = a^{m+n}
\]

So, we add the exponents:

\[
5^2 \cdot 5^{-3} \cdot 5^{-1} = 5^{2 + (-3) + (-1)} = 5^{2 - 3 - 1} = 5^{-2}
\]

Therefore, the simplified expression is:

\[
5^{-2}
\]

This can also be written as:

\[
\frac{1}{5^2} = \frac{1}{25}
\]

Thus, the value of the expression is \(\frac{1}{25}\).

Would you like more details or have any questions?

Here are some related questions for you:
1. How do negative exponents affect the value of a number?
2. What are the properties of exponents when multiplying powers of the same base?
3. How can you convert a negative exponent to a fraction?
4. What would the result be if one of the exponents were positive instead of negative?
5. How does this rule apply to bases other than 5?

**Tip:** When working with powers of the same base, always remember to add or subtract the exponents according to the operation (multiplication or division).

Simplify the expression: 5^2 · 5^-3 · 5^-1

Learn how to simplify the expression 5^2 · 5^-3 · 5^-1 using the laws of exponents. This solution demonstrates how to add the exponents when multiplying powers of the same base, resulting in a final value of 1/25. Suitable for students in Grades 6-8.

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