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

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Exponents

This article will explore how to simplify the expression (-2x^5y^2)^4. We will break down the process step-by-step, explaining the rules of exponents involved.

Understanding the Rules of Exponents

Before we delve into the problem, let's refresh our understanding of some key exponent rules:

• Product of powers: (a^m) * (a^n) = a^(m+n)
• Power of a product: (ab)^n = a^n * b^n
• Power of a power: (a^m)^n = a^(m*n)

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

1. Apply the power of a product rule: (-2x^5y^2)^4 = (-2)^4 * (x^5)^4 * (y^2)^4

2. Apply the power of a power rule: (-2)^4 * (x^5)^4 * (y^2)^4 = 16 * x^(54) * y^(24)

3. Simplify: 16 * x^(54) * y^(24) = 16x^20y^8

Conclusion

By applying the rules of exponents, we were able to simplify the expression (-2x^5y^2)^4 to 16x^20y^8. Remember to break down complex expressions into smaller parts and apply the appropriate rules to achieve a simplified form.