https://file.aiquickdraw.com/mathbot/file/1725179285514y2d1s6ip.jpg

The image you've provided contains a mathematical problem involving exponents and possibly some simplification steps. Based on the visual analysis, I will rewrite the problem and solve it for you.

### Problem from the Image:
\[ 
\text{Given:} \quad (-2a^2b^3) \times 2a^3b^{-4} \times -3a^{-1}b^2 
\]

### Steps to Solve:

1. **Group the coefficients:**
   \[
   (-2) \times 2 \times (-3) = -4 \times (-3) = 12
   \]

2. **Combine the exponents for \(a\) (using the rule \(a^m \times a^n = a^{m+n}\)):**
   \[
   a^2 \times a^3 \times a^{-1} = a^{(2+3-1)} = a^4
   \]

3. **Combine the exponents for \(b\) (using the rule \(b^m \times b^n = b^{m+n}\)):**
   \[
   b^3 \times b^{-4} \times b^2 = b^{(3-4+2)} = b^1 = b
   \]

4. **Final expression:**
   \[
   \text{The simplified expression is: } 12a^4b
   \]

### Solution:
\[
\boxed{12a^4b}
\]

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

Here are some related questions to consider:
1. What happens when the exponents are negative in similar problems?
2. How would the solution change if one of the coefficients was a fraction?
3. Can you generalize the process for combining terms with exponents?
4. How does changing the order of multiplication affect the final answer?
5. What rules govern the combination of exponents in multiplication versus division?

**Tip:** Always combine like terms and exponents carefully, keeping track of any negative signs to avoid mistakes.

Learn how to simplify the expression -2a^2b^3 * 2a^3b^-4 * -3a^-1b^2 step-by-step with detailed explanations of combining like terms and exponents. This problem involves exponents and polynomial multiplication, suitable for high school level mathematics.

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