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(-x^2)^5(-2x^2y^3)^3

2 min read Jun 16, 2024
(-x^2)^5(-2x^2y^3)^3

Simplifying Exponential Expressions: (-x^2)^5(-2x^2y^3)^3

This article will guide you through the process of simplifying the expression (-x^2)^5(-2x^2y^3)^3.

Understanding the Rules of Exponents

Before we dive into the simplification, let's refresh our memory on some key 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)

Step-by-Step Simplification

  1. Distribute the outer exponents: Using the power of a product rule, we can distribute the exponents:

    • (-x^2)^5 = (-1)^5 * (x^2)^5 = -x^10
    • (-2x^2y^3)^3 = (-2)^3 * (x^2)^3 * (y^3)^3 = -8x^6y^9

  2. Multiply the simplified terms: Now we have:

    • -x^10 * -8x^6y^9

  3. Combine like terms: Using the product of powers rule, we add the exponents of the same variables:

    • -1 * -8 * x^(10+6) * y^9 = 8x^16y^9

The Final Result

Therefore, the simplified form of (-x^2)^5(-2x^2y^3)^3 is 8x^16y^9.

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