(2a^2b)(4ab^2) Simplified

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (2a²b)(4ab²)

This article will guide you through simplifying the expression (2a²b)(4ab²).

Understanding the Basics

The expression involves multiplying two monomials. A monomial is a single term algebraic expression consisting of a coefficient and one or more variables raised to non-negative integer exponents.

Applying the Rules of Exponents

To simplify the expression, we use the following rules of exponents:

• Product of powers: x^m * x^n = x^(m+n)
• Commutative property of multiplication: a * b = b * a
• Associative property of multiplication: (a * b) * c = a * (b * c)

Step-by-Step Simplification

1. Rearrange the terms: (2a²b)(4ab²) = 2 * 4 * a² * a * b * b²

2. Combine the coefficients: 2 * 4 * a² * a * b * b² = 8 * a² * a * b * b²

3. Apply the product of powers rule: 8 * a² * a * b * b² = 8 * a^(2+1) * b^(1+2)

4. Simplify: 8 * a^(2+1) * b^(1+2) = 8a³b³

Conclusion

Therefore, the simplified expression of (2a²b)(4ab²) is 8a³b³. By understanding the rules of exponents and applying them systematically, we can effectively simplify complex algebraic expressions.