Simplifying the Expression (2a²b)(4ab²)
This article will guide you through simplifying the expression (2a²b)(4ab²).
Understanding the Expression
The expression (2a²b)(4ab²) involves multiplying two terms, each containing variables and coefficients. Let's break down each term:

2a²b:
 2 is the coefficient.
 a² represents the variable 'a' raised to the power of 2.
 b represents the variable 'b' raised to the power of 1 (which is not explicitly written).

4ab²:
 4 is the coefficient.
 a represents the variable 'a' raised to the power of 1.
 b² represents the variable 'b' raised to the power of 2.
Applying the Rules of Exponents
To simplify the expression, we need to use the rules of exponents:

Product of Powers: When multiplying powers with the same base, add the exponents.
 Example: a² * a = a^(2+1) = a³

Commutative Property: The order of multiplication does not affect the result.
 Example: 2 * 3 = 3 * 2
Simplifying the Expression
 Multiply the coefficients: 2 * 4 = 8
 Multiply the 'a' terms: a² * a = a^(2+1) = a³
 Multiply the 'b' terms: b * b² = b^(1+2) = b³
Final Result
By combining the simplified terms, we get the final result: 8a³b³