To simplify the expression \((4x^2y^{-3})(2x^{-3}y^2)\), follow these steps:

1. **Multiply the constants**:  
   \(4 \times 2 = 8\)

2. **Combine the \(x\) terms**:  
   \(x^2 \times x^{-3} = x^{2 + (-3)} = x^{-1}\)

3. **Combine the \(y\) terms**:  
   \(y^{-3} \times y^2 = y^{-3 + 2} = y^{-1}\)

Now, put everything together:

\[
(4x^2y^{-3})(2x^{-3}y^2) = 8x^{-1}y^{-1}
\]

Finally, express the negative exponents as fractions:

\[
8x^{-1}y^{-1} = \frac{8}{xy}
\]

So, the simplified expression is \(\frac{8}{xy}\).

Would you like further details on any steps or have any questions?

Here are five related questions you might find useful:
1. How would the expression change if one of the exponents was positive?
2. What happens if you multiply two expressions with the same base but different exponents?
3. How do you handle negative exponents in a fraction?
4. How do you simplify an expression with both positive and negative exponents?
5. Can you simplify \((x^4y^{-2})(3x^{-1}y^3)\)?

**Tip**: Always simplify exponents first before combining the terms when multiplying expressions.

Discover how to simplify the expression (4x^2y^-3)(2x^-3y^2) by applying the product of powers rule and simplifying negative exponents. This step-by-step guide is ideal for students in Grades 8-10, focusing on key algebraic concepts.

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