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

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

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

In mathematics, simplifying expressions is a crucial skill. Let's break down how to simplify the expression (-2x^3y^5)^2.

Understanding the Basics

  • Exponents: An exponent indicates how many times a base number is multiplied by itself. For example, x^2 means x * x.
  • Parentheses: When an expression is enclosed in parentheses and raised to a power, we apply the exponent to every term inside the parentheses.

Step-by-Step Simplification

  1. Distribute the exponent:
    (-2x^3y^5)^2 = (-2)^2 * (x^3)^2 * (y^5)^2

  2. Apply the power of a power rule: When raising a power to another power, multiply the exponents. (-2)^2 * (x^(32)) * (y^(52)) = 4 * x^6 * y^10

  3. Final result: The simplified expression is 4x^6y^10.

Key Points

  • Remember to apply the exponent to all terms inside the parentheses, including the coefficient.
  • The order of operations (PEMDAS/BODMAS) is crucial for correct simplification.
  • Practice with different expressions to solidify your understanding.

This process demonstrates the power of mathematical rules and the importance of understanding exponents and their applications.

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