To simplify the expression \(\frac{6x^3 y^2}{2x}\), follow these steps:

1. First, divide the coefficients: \(\frac{6}{2} = 3\).
2. Then, apply the rule of exponents for the \(x\)-terms. When dividing powers of the same base, subtract the exponents: \(x^3 / x = x^{3-1} = x^2\).
3. The \(y^2\) term remains unchanged because there is no \(y\) term in the denominator.

Thus, the simplified expression is:
\[
3x^2 y^2
\]

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 is the rule for multiplying powers with the same base?
3. How do you handle variables in both the numerator and denominator?
4. Can you simplify \(6x^3 y^2 z^4 / 2x z^2\)?
5. How do you factor polynomials with multiple variables?

**Tip:** When simplifying, always handle the coefficients and variables separately for clarity!

Learn how to simplify the expression 6x^3 y^2 / 2x using algebraic techniques such as dividing coefficients and applying exponent rules. This problem covers important algebra concepts and is suitable for students in Grades 8-10.

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