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(-8x^4y^3)(2x^5y^2)+7x^9y^5

less than a minute read Jun 16, 2024
(-8x^4y^3)(2x^5y^2)+7x^9y^5

Simplifying Expressions with Exponents

This article will demonstrate how to simplify the expression (-8x⁴y³)(2x⁵y²) + 7x⁹y⁵. We'll break down the steps using the rules of exponents.

Understanding the Rules of Exponents

Before we begin, let's review some key rules of exponents:

  • Product of Powers: xᵃ * xᵇ = xᵃ⁺ᵇ
  • Power of a Product: (xy)ᵃ = xᵃyᵃ

Simplifying the Expression

  1. Multiply the coefficients:
    (-8)(2) = -16

  2. Multiply the x terms using the Product of Powers rule: x⁴ * x⁵ = x⁴⁺⁵ = x⁹

  3. Multiply the y terms using the Product of Powers rule: y³ * y² = y³⁺² = y⁵

  4. Combine the results from steps 1-3: (-8x⁴y³)(2x⁵y²) = -16x⁹y⁵

  5. Add the remaining term: -16x⁹y⁵ + 7x⁹y⁵

  6. Combine like terms: (-16 + 7)x⁹y⁵ = -9x⁹y⁵

Final Answer

The simplified expression is -9x⁹y⁵.

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