(4ab^2)^3(-2a^5)

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions: (4ab^2)^3(-2a^5)

This article will guide you through simplifying the expression (4ab^2)^3(-2a^5). We'll break down each step to make it easy to understand.

Understanding the Rules

Before we start, let's recall some important exponent rules:

• Power of a product: (ab)^n = a^n * b^n
• Power of a power: (a^m)^n = a^(m*n)
• Product of powers: a^m * a^n = a^(m+n)

Simplifying the Expression

1. Apply the power of a product rule: (4ab^2)^3 = 4^3 * a^3 * (b^2)^3

2. Apply the power of a power rule: 4^3 * a^3 * (b^2)^3 = 64a^3b^6

3. Multiply the result by -2a^5: 64a^3b^6 * (-2a^5) = -128a^8b^6

Final Answer

Therefore, the simplified expression of (4ab^2)^3(-2a^5) is -128a^8b^6.