https://file.aiquickdraw.com/mathbot/file/1726553880703njjipsvz.jpg

The problem in the image shows the expression \( 3a^{-2} \) being transformed in some way. Let’s break down the problem step-by-step:

Given:
\[
3a^{-2}
\]

### Step-by-Step Simplification
1. **Rewrite the Negative Exponent:** \( a^{-2} \) can be rewritten using the rule \( x^{-n} = \frac{1}{x^n} \). So,
   \[
   3a^{-2} = 3 \times \frac{1}{a^2} = \frac{3}{a^2}.
   \]

2. **Comparing to the Given Work in the Image:** It appears that the final answer in the image is simplified to:
   \[
   \frac{3}{9a^2}.
   \]

3. **Further Simplification:** Notice that \( 9a^2 \) is a product of \( 9 \) and \( a^2 \). However, the numerator and denominator both have a common factor of \( 3 \):
   \[
   \frac{3}{9a^2} = \frac{1}{3a^2}.
   \]

### Final Simplified Answer
Thus, the expression \( 3a^{-2} \) simplifies to \( \frac{3}{a^2} \) or, as shown in the image, \( \frac{1}{3a^2} \) after adjusting the denominator to \( 9a^2 \).

Would you like more details or have any questions?

### Follow-Up Questions
1. How do you handle negative exponents in general?
2. What are the rules for simplifying fractions involving variables?
3. Can you apply the same rules to simplify \( 4b^{-3} \)?
4. What happens when you multiply two terms with negative exponents?
5. How would you simplify \( 6x^{-4}y^{-2} \)?

### Tip
When dealing with negative exponents, always rewrite them as fractions to make further simplification easier.

Learn how to simplify the algebraic expression 3a^{-2} using exponent rules. This step-by-step guide covers simplifying negative exponents, turning them into fractions, and reducing the expression further. Suitable for students in Grades 8-10.

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