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

less than a minute read Jun 16, 2024
(-2x^4)^3(-2x^2)^2

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

This article will walk through the process of simplifying the expression (-2x^4)^3(-2x^2)^2.

Understanding the Properties

To simplify this expression, we need to understand a couple of key properties of exponents:

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

Applying the Properties

  1. Distribute the exponents:

    • (-2x^4)^3 = (-2)^3 * (x^4)^3
    • (-2x^2)^2 = (-2)^2 * (x^2)^2

  2. Simplify using the power of a power rule:

    • (-2)^3 * (x^4)^3 = -8 * x^(4*3) = -8x^12
    • (-2)^2 * (x^2)^2 = 4 * x^(2*2) = 4x^4

  3. Multiply the simplified terms:

    • -8x^12 * 4x^4 = -32x^(12+4) = -32x^16

Final Result

Therefore, the simplified expression is -32x^16.

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