To simplify the expression \( 4x^{-2} \), we need to apply the negative exponent rule, which states that \( a^{-n} = \frac{1}{a^n} \). Here's the step-by-step process:

1. Start with the given expression:
   \[
   4x^{-2}
   \]

2. The negative exponent \( -2 \) applies only to \( x \), not to the \( 4 \). So, we can rewrite the expression as:
   \[
   4 \cdot x^{-2}
   \]

3. Using the negative exponent rule \( x^{-n} = \frac{1}{x^n} \), we can rewrite \( x^{-2} \) as:
   \[
   x^{-2} = \frac{1}{x^2}
   \]

4. Substitute this back into the expression:
   \[
   4 \cdot \frac{1}{x^2}
   \]

5. This simplifies to:
   \[
   \frac{4}{x^2}
   \]

Therefore, the simplified expression is:

\[
4x^{-2} = \frac{4}{x^2}
\]

Would you like more details or have any questions about this process?

### Related Questions:

1. How would you simplify \( 5x^{-3} \)?
2. What is the result of \( 7y^{-1} \)?
3. How does the negative exponent rule apply to a product of variables, like \( 6x^{-1}y^{-2} \)?
4. Can you solve \( 2x^{-1}y^2 \) and express it as a fraction?
5. What happens if you have both negative and positive exponents in the same expression, such as \( 3x^{-2}y^3 \)?

### Tip:
When dealing with negative exponents, remember to apply the negative exponent rule to each term separately. This will help in accurately simplifying the expression.

Learn how to simplify the expression 4x^-2 step-by-step with detailed explanations and examples. This problem covers key concepts in exponents, including the negative exponent rule. Suitable for students in Grades 7-9.

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