%5E2.jpeg "(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
- Distribute the exponent: The exponent outside the parentheses applies to everything inside: (4x³y⁴)² = 4² * (x³)² * (y⁴)²
- Simplify each term: 4² = 16, (x³)² = x⁶, (y⁴)² = y⁸
- 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.