We need to simplify the expression: 

\[
\frac{20x^9y}{6x} \times -4xy^2
\]

### Step 1: Simplify \(\frac{20x^9y}{6x}\)

Divide the coefficients \(20\) and \(6\), and simplify the powers of \(x\):

\[
\frac{20}{6} = \frac{10}{3}, \quad \frac{x^9}{x} = x^{9-1} = x^8
\]

So the simplified expression is:

\[
\frac{10x^8y}{3}
\]

### Step 2: Multiply by \(-4xy^2\)

Now multiply the result by \(-4xy^2\):

\[
\frac{10x^8y}{3} \times (-4xy^2)
\]

Multiply the coefficients:

\[
\frac{10 \times (-4)}{3} = \frac{-40}{3}
\]

Now, multiply the variables:
- \(x^8 \times x = x^{8+1} = x^9\)
- \(y \times y^2 = y^{1+2} = y^3\)

So the final simplified expression is:

\[
\frac{-40x^9y^3}{3}
\]

### Final Answer:
\[
\frac{-40x^9y^3}{3}
\]

Would you like more details on this process or any specific steps?

Here are 5 questions related to this problem:
1. How do you simplify fractions with variable powers?
2. What is the process for multiplying terms with exponents?
3. How do negative coefficients affect expressions?
4. How do you multiply two polynomials?
5. Can you explain the rules of exponents in more detail?

**Tip:** When dividing powers of the same base, subtract the exponents!

Learn how to simplify the algebraic expression 20x^9y/6x × -4xy^2 with a step-by-step solution. This solution covers key algebraic concepts such as simplifying fractions with variable powers and applying exponent rules. Suitable for students in Grades 9-10.

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