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

less than a minute read Jun 16, 2024
(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

  1. Apply the power of a product rule to (4ab^3)^2: (4ab^3)^2 = 4^2 * a^2 * (b^3)^2 = 16a^2b^6

  2. 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.

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