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

less than a minute read Jun 16, 2024
(-3x^5y^2)^3

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

This expression involves raising a monomial to a power. To simplify it, we need to apply the rules of exponents.

Understanding the Rules

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

Simplifying the Expression

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

  2. Apply the product of powers rule: (-3)^3 * (x^5)^3 * (y^2)^3 = -27 * x^(53) * y^(23)

  3. Simplify: -27 * x^(53) * y^(23) = -27x^15y^6

Conclusion

Therefore, the simplified form of (-3x^5y^2)^3 is -27x^15y^6.

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