(-6xy^4)^3

Jasonbradley

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Jun 16, 2024

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Simplifying (-6xy^4)^3

In mathematics, simplifying expressions often involves applying the rules of exponents. Let's break down how to simplify the expression (-6xy^4)^3.

Understanding the Rules

The key rules we'll use are:

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

Step-by-Step Solution

1. Apply the power of a product rule: (-6xy^4)^3 = (-6)^3 * x^3 * (y^4)^3

2. Apply the power of a power rule: (-6)^3 * x^3 * (y^4)^3 = -216 * x^3 * y^(4*3)

3. Simplify: -216 * x^3 * y^(4*3) = -216x^3y^12

Conclusion

Therefore, the simplified form of (-6xy^4)^3 is -216x^3y^12. Remember, the process involves applying the rules of exponents systematically to achieve a simplified expression.