The given expression is \((3a^2b^2)(ab^4)\). To simplify, we'll follow these steps:

1. **Multiply the constants**: In this case, there is only a constant 3.

2. **Multiply the powers of \(a\)**: Apply the rule of exponents that states \(a^m \times a^n = a^{m+n}\).
   - \(a^2 \times a^1 = a^{2+1} = a^3\)

3. **Multiply the powers of \(b\)**: Again, apply the exponent rule \(b^m \times b^n = b^{m+n}\).
   - \(b^2 \times b^4 = b^{2+4} = b^6\)

Now, multiplying everything together, the simplified expression becomes:

\[
3a^3b^6
\]

### Final Answer:
\[
3a^3b^6
\]

Would you like more details on this, or do you have any other questions?

Here are 5 related questions for further practice:
1. Simplify \((2a^3b)(5a^2b^4)\).
2. What is the simplified form of \((4a^2b^3)(2ab^2)\)?
3. How do you simplify \((6a^4b^2)(3a^2b^5)\)?
4. Multiply and simplify \((a^5b^2)(ab^3)\).
5. What is the result of \((2a^2b^2)(3ab^3)\)?

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

Master how to simplify the expression (3a^2b^2)(ab^4) using exponent rules. This solution walks through the multiplication of exponents step-by-step, perfect for algebra students in Grades 8-10.

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