To simplify the expression \((3a^2b^3)(2ab)\), you can multiply the coefficients (numbers) and the variables separately.

### Steps:
1. **Multiply the coefficients**:
   \[
   3 \times 2 = 6
   \]

2. **Multiply the variables**:
   - For \(a\): \(a^2 \times a = a^{2+1} = a^3\)
   - For \(b\): \(b^3 \times b = b^{3+1} = b^4\)

3. **Combine the results**:
   \[
   (3a^2b^3)(2ab) = 6a^3b^4
   \]

So, the simplified expression is **\(6a^3b^4\)**.

Would you like to go over any details or have any questions?

Here are 5 related questions you might find interesting:
1. How do you simplify expressions with multiple variables and exponents?
2. What are the rules for multiplying exponents in algebraic expressions?
3. How would you simplify \((4x^3y^2)(5xy^3)\)?
4. What happens when you multiply terms with different bases?
5. How do you simplify expressions that involve division of exponents?

**Tip:** When multiplying terms with the same base, simply add the exponents!

Learn how to simplify the expression (3a²b³)(2ab) with a detailed step-by-step solution. This problem involves algebraic concepts such as multiplication of polynomials and exponents. Suitable for students in Grades 7-9.

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