%5E3(-2a%5E5).jpeg "(4ab^2)^3(-2a^5)")
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
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Apply the power of a product rule: (4ab^2)^3 = 4^3 * a^3 * (b^2)^3
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Apply the power of a power rule: 4^3 * a^3 * (b^2)^3 = 64a^3b^6
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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.