Let's simplify the expression: 

\[
\frac{-4x^4y^2}{2xy^2}
\]

### Step-by-step simplification:

1. **Divide the constants**: 
   \[
   \frac{-4}{2} = -2
   \]

2. **Simplify the powers of \(x\)**: 
   \[
   \frac{x^4}{x} = x^{4-1} = x^3
   \]

3. **Simplify the powers of \(y\)**: 
   \[
   \frac{y^2}{y^2} = 1
   \]

Now putting everything together:
\[
-2x^3 \times 1 = -2x^3
\]

So, the simplified expression is:

\[
-2x^3
\]

Would you like further details or have any questions? 

Here are 5 related questions:
1. How do you simplify expressions involving exponents?
2. What is the rule for dividing powers with the same base?
3. How do constants affect algebraic expressions?
4. Can this expression be simplified further if different terms are added?
5. How would you handle negative exponents in a similar problem?

**Tip**: Always simplify constants and variables separately before combining them!

Learn how to simplify the algebraic expression 4x^4y^2 / 2xy^2 with a detailed step-by-step solution. This problem covers key concepts such as the power rule for exponents and simplifying rational expressions. Suitable for students in Grades 8-10.

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