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(4x^5y)^2

2 min read Jun 16, 2024
(4x^5y)^2

Simplifying (4x^5y)^2

In mathematics, simplifying expressions often involves applying rules of exponents. Let's break down how to simplify the expression (4x^5y)^2.

Understanding the Rules

  • Power of a Product: When raising a product to a power, we raise each factor to that power: (ab)^n = a^n * b^n
  • Power of a Power: When raising a power to another power, we multiply the exponents: (a^m)^n = a^(m*n)

Applying the Rules

  1. Apply the Power of a Product rule: (4x^5y)^2 = 4^2 * (x^5)^2 * y^2

  2. Apply the Power of a Power rule: 4^2 * (x^5)^2 * y^2 = 16 * x^(5*2) * y^2

  3. Simplify: 16 * x^(5*2) * y^2 = 16x^10y^2

Conclusion

Therefore, the simplified form of (4x^5y)^2 is 16x^10y^2. This process demonstrates the importance of understanding and applying exponent rules to manipulate and simplify expressions effectively.

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