To simplify the expression \( \frac{1}{x^4y^2} \times x^2y^3 \), follow these steps:

1. Multiply the numerators and denominators separately:
   \[
   \frac{x^2y^3}{x^4y^2}
   \]

2. Simplify by canceling out common terms:

   - For the \(x\) terms: \( \frac{x^2}{x^4} = \frac{1}{x^{2}} \)
   - For the \(y\) terms: \( \frac{y^3}{y^2} = y \)

   So the expression simplifies to:

   \[
   \frac{y}{x^2}
   \]

The simplified expression is \( \frac{y}{x^2} \).

Would you like more details or have any questions? Here are some related questions:

1. How do you simplify expressions with negative exponents?
2. What are the properties of exponents used in multiplication and division?
3. How do you simplify expressions with multiple variables?
4. Can you apply this simplification process to more complex algebraic fractions?
5. What happens when the exponents are fractional?

**Tip:** Always reduce expressions by canceling common factors to simplify your work.

Learn how to simplify the expression 1/x^4y^2 × x^2y^3 step-by-step. This problem involves algebraic manipulation of exponents and fractions. Suitable for students in Grades 7-9.

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