%5E2(-3a%5E5).jpeg "(4ab^3)^2(-3a^5)")
Simplifying the Expression: (4ab^3)^2(-3a^5)
This article will guide you through simplifying the expression (4ab^3)^2(-3a^5).
Understanding the Properties
Before we begin, let's recall some key properties of exponents:
- 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
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Apply the power of a product rule to (4ab^3)^2: (4ab^3)^2 = 4^2 * a^2 * (b^3)^2 = 16a^2b^6
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Multiply the simplified term by (-3a^5): 16a^2b^6 * (-3a^5) = -48a^7b^6
Final Result
Therefore, the simplified expression of (4ab^3)^2(-3a^5) is -48a^7b^6.