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

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

Simplifying Expressions with Exponents

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

Understanding the Basics

Before we dive into the simplification process, let's recall some key rules 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)

Step-by-Step Simplification

  1. Simplify the exponents:

    • (-2^2) = (-2)(-2) = 4
    • (-3^2) = (-3)(-3) = 9

  2. Rewrite the expression:

    • The expression now becomes: (4x^3y^4)(9x^4y^4)

  3. Apply the product of powers rule:

    • For the x terms: x^3 * x^4 = x^(3+4) = x^7
    • For the y terms: y^4 * y^4 = y^(4+4) = y^8

  4. Combine the terms:

    • The expression simplifies to: 4 * 9 * x^7 * y^8 = 36x^7y^8

Final Result

Therefore, the simplified form of (-2^2x^3y^4)((-3)^2x^4y^4) is 36x^7y^8.

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