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

Jasonbradley

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Jun 16, 2024

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

In mathematics, simplifying expressions often involves applying the rules of exponents. Let's explore how to simplify the expression (-2x^5y^3)^3.

Understanding the Rules

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

Applying the Rules

1. Apply the power of a product rule: (-2x^5y^3)^3 = (-2)^3 * (x^5)^3 * (y^3)^3

2. Apply the power of a power rule: (-2)^3 * (x^5)^3 * (y^3)^3 = -8 * x^(53) * y^(33)

3. Simplify: -8 * x^(53) * y^(33) = -8x^15y^9

Conclusion

Therefore, the simplified form of (-2x^5y^3)^3 is -8x^15y^9. By applying the rules of exponents, we can efficiently simplify complex expressions and express them in a more compact form.