To simplify the expression \( x^{-2} \cdot \frac{1}{x} \), follow these steps:

1. Rewrite \(\frac{1}{x}\) as \(x^{-1}\):
   \[
   x^{-2} \cdot x^{-1}
   \]

2. Combine the exponents using the property \(a^m \cdot a^n = a^{m+n}\):
   \[
   x^{-2 - 1} = x^{-3}
   \]

Thus, the simplified expression is:
\[
x^{-3}
\]

If you need further details or have any questions, feel free to ask! Here are some related questions:

1. What are the properties of exponents?
2. How would you simplify \(x^{-3} \cdot x^2\)?
3. What is the value of \(x^{-3}\) when \(x = 2\)?
4. Can you explain how to convert negative exponents to positive ones?
5. How does this simplification apply to equations involving variables? 

**Tip:** Remember that multiplying terms with the same base involves adding their exponents!

Discover how to simplify the expression x^{-2} \cdot \frac{1}{x} step-by-step. This guide covers key concepts in algebra and the properties of exponents, making it suitable for students in Grades 6-8.

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