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(2x^3y^5)^3

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

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

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

Understanding the Concepts

  • Exponents: An exponent indicates how many times a base number is multiplied by itself. For example, x^3 means x multiplied by itself three times (x * x * x).
  • Power of a product: When a product is raised to a power, each factor within the product is raised to that power. For example, (ab)^n = a^n * b^n.

Applying the Concepts

  1. Distribute the exponent: Using the power of a product rule, we distribute the exponent 3 to each factor within the parentheses: (2x^3y^5)^3 = 2^3 * (x^3)^3 * (y^5)^3

  2. Simplify each factor:

    • 2^3 = 2 * 2 * 2 = 8
    • (x^3)^3 = x^(33) = x^9 (using the power of a power rule: (a^m)^n = a^(mn))
    • (y^5)^3 = y^(5*3) = y^15

  3. Combine the simplified factors: 8 * x^9 * y^15 = 8x^9y^15

Conclusion

Therefore, the simplified form of (2x^3y^5)^3 is 8x^9y^15. This process demonstrates the importance of understanding exponent rules and their application in simplifying complex expressions.

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