(5ab)(-2a^2b)^3

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (5ab)(-2a^2b)^3

This article will guide you through the process of simplifying the expression (5ab)(-2a^2b)^3. We will use the rules of exponents to break down the expression step-by-step.

Understanding the Rules of Exponents

Before we dive into the simplification, let's review some key exponent rules:

• Product of powers: x^m * x^n = x^(m+n)
• Power of a product: (xy)^n = x^n * y^n
• Power of a power: (x^m)^n = x^(m*n)

Simplifying the Expression

1. Focus on the exponent: We begin by simplifying the term (-2a^2b)^3 using the power of a product rule: (-2a^2b)^3 = (-2)^3 * (a^2)^3 * (b)^3

2. Apply the power of a power rule: (-2)^3 * (a^2)^3 * (b)^3 = -8 * a^(2*3) * b^3 = -8a^6b^3

3. Multiply the remaining terms: Now we have: (5ab)(-8a^6b^3) = (5 * -8) * (a * a^6) * (b * b^3)

4. Combine like terms: (5 * -8) * (a * a^6) * (b * b^3) = -40a^7b^4

Final Result

The simplified form of the expression (5ab)(-2a^2b)^3 is -40a^7b^4.