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(-4xy)^3(-2x^2)^3

2 min read Jun 16, 2024
(-4xy)^3(-2x^2)^3

Simplifying the Expression (-4xy)^3(-2x^2)^3

This article will guide you through simplifying the expression (-4xy)^3(-2x^2)^3.

Understanding the Properties of Exponents

Before we start, let's review some key properties of exponents:

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

Simplifying the Expression

  1. Apply the power of a product property:

    • (-4xy)^3 = (-4)^3 * x^3 * y^3 = -64x^3y^3
    • (-2x^2)^3 = (-2)^3 * (x^2)^3 = -8x^6

  2. Substitute the simplified terms back into the original expression:

    • (-4xy)^3(-2x^2)^3 = -64x^3y^3 * -8x^6

  3. Apply the product of powers property:

    • -64x^3y^3 * -8x^6 = 512x^(3+6)y^3 = 512x^9y^3

Final Result

Therefore, the simplified form of the expression (-4xy)^3(-2x^2)^3 is 512x^9y^3.

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