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(-3x^3y^4)^2

2 min read Jun 16, 2024
(-3x^3y^4)^2

Simplifying (-3x^3y^4)^2

In mathematics, simplifying expressions is a fundamental skill. Let's break down the process of simplifying the expression (-3x^3y^4)^2.

Understanding the Rules

  • Exponents: An exponent indicates repeated multiplication. For example, x^2 means x multiplied by itself (x * x).
  • Power of a Product: When a product is raised to a power, each factor within the product is raised to that power. This is represented as (ab)^n = a^n * b^n.
  • Power of a Power: When a power is raised to another power, the exponents are multiplied. This is represented as (a^m)^n = a^(m*n).

Simplifying the Expression

  1. Apply the Power of a Product Rule: (-3x^3y^4)^2 = (-3)^2 * (x^3)^2 * (y^4)^2

  2. Apply the Power of a Power Rule: (-3)^2 * (x^3)^2 * (y^4)^2 = 9 * x^(32) * y^(42)

  3. Simplify: 9 * x^(32) * y^(42) = 9x^6y^8

Conclusion

Therefore, the simplified form of (-3x^3y^4)^2 is 9x^6y^8. Remember to apply the relevant rules of exponents when simplifying expressions to achieve accurate results.

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