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(4x^3y^4)^2

less than a minute read Jun 16, 2024
(4x^3y^4)^2

Simplifying Expressions with Exponents: (4x³y⁴)²

In mathematics, understanding how to simplify expressions involving exponents is crucial. One common example is simplifying expressions like (4x³y⁴)². Let's break down the steps:

Understanding the Rules of Exponents

  • Product of Powers: When multiplying powers with the same base, add the exponents: xᵃ * xᵇ = xᵃ⁺ᵇ
  • Power of a Power: When raising a power to another power, multiply the exponents: (xᵃ)ᵇ = xᵃᵇ

Applying the Rules

  1. Distribute the exponent: The exponent outside the parentheses applies to everything inside: (4x³y⁴)² = 4² * (x³)² * (y⁴)²
  2. Simplify each term: 4² = 16, (x³)² = x⁶, (y⁴)² = y⁸
  3. Combine the terms: 16 * x⁶ * y⁸ = 16x⁶y⁸

Conclusion

Therefore, the simplified form of (4x³y⁴)² is 16x⁶y⁸. This process demonstrates the fundamental rules of exponents and how they can be used to simplify complex expressions.

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