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Let's simplify the given expression:

\[
2x^3 y^{-3} \cdot 2x^{-1} y^3
\]

### Step-by-step Solution:
1. **Multiply the coefficients**:
   - \(2 \cdot 2 = 4\).

2. **Combine the like terms**:
   - For \(x\):
     \[
     x^3 \cdot x^{-1} = x^{3 + (-1)} = x^2.
     \]
   - For \(y\):
     \[
     y^{-3} \cdot y^3 = y^{-3 + 3} = y^0 = 1.
     \]

3. **Combine everything**:
   \[
   4 \cdot x^2 \cdot 1 = 4x^2.
   \]

### Final Answer:
\[
4x^2
\]

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

Here are some related questions:
1. What happens when you multiply powers with the same base?
2. How do you handle negative exponents in multiplication?
3. Why does \(y^0\) equal 1 in the simplification process?
4. What are the rules for combining coefficients in algebraic expressions?
5. How can you simplify expressions with multiple variables?

**Tip:** Always combine like terms by adding exponents when multiplying expressions with the same base.

Simplify the expression: 2x^3 y^{-3} * 2x^{-1} y^3 using exponent rules and positive exponents only.

Learn how to simplify the expression 2x^3 y^{-3} * 2x^{-1} y^3 by applying exponent laws. This solution includes multiplying coefficients and adding exponents of the same base, and is suitable for students in Grades 8-10.

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