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(-3x^4y^5)^2

2 min read Jun 16, 2024
(-3x^4y^5)^2

Simplifying (-3x^4y^5)^2

In this article, we will explore the simplification of the expression (-3x^4y^5)^2. Understanding the rules of exponents is crucial for simplifying expressions like this.

Understanding the Rules of Exponents

Here are the key rules of exponents that we'll use:

  • Product of Powers: (x^m) * (x^n) = x^(m+n)
  • Power of a Power: (x^m)^n = x^(m*n)
  • Power of a Product: (xy)^n = x^n * y^n

Simplifying the Expression

Let's break down the simplification step-by-step:

  1. Apply the Power of a Product rule: (-3x^4y^5)^2 = (-3)^2 * (x^4)^2 * (y^5)^2

  2. Apply the Power of a Power rule: (-3)^2 * (x^4)^2 * (y^5)^2 = 9 * x^(42) * y^(52)

  3. Simplify: 9 * x^(42) * y^(52) = 9x^8y^10

Conclusion

Therefore, the simplified form of (-3x^4y^5)^2 is 9x^8y^10. Remember, by applying the rules of exponents, we can efficiently simplify complex expressions.

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