The given expression is \((2p^2q)(2pq^2)\). To simplify it, let's apply the properties of multiplication and powers:

1. First, multiply the constants:
   \[
   2 \times 2 = 4
   \]

2. Next, handle the variables:
   - Multiply \(p^2\) by \(p\):
     \[
     p^2 \times p = p^{2+1} = p^3
     \]
   - Multiply \(q\) by \(q^2\):
     \[
     q \times q^2 = q^{1+2} = q^3
     \]

3. Combine all the results:
   \[
   4p^3q^3
   \]

Thus, the simplified expression is:
\[
4p^3q^3
\]

Would you like any further details or have any questions?

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Here are 5 related questions:

1. How do you simplify expressions with different powers of variables?
2. What is the rule for multiplying exponents with the same base?
3. Can you factor expressions like the one given?
4. How do you simplify expressions with multiple variables and constants?
5. How do negative exponents affect multiplication?

**Tip:** When multiplying terms with the same base, simply add the exponents to combine them.

Learn how to simplify the polynomial expression (2p^2q)(2pq^2) step-by-step. This problem covers the multiplication of polynomials, including key concepts such as combining powers of the same base. Ideal for students in Grades 7-9.

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