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

less than a minute read Jun 16, 2024
(-3x^2y^4)^5

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

This expression involves raising a monomial to a power. Let's break down the simplification step by step.

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. Distribute the exponent: Using the "power of a product" rule, we apply the exponent 5 to each factor inside the parentheses: (-3)^5 * (x^2)^5 * (y^4)^5

  2. Simplify the exponents: Applying the "power of a power" rule, we multiply the exponents: (-3)^5 * x^(25) * y^(45)

  3. Calculate the numerical part: (-3)^5 = -243 -243 * x^10 * y^20

Final Result

The simplified form of (-3x^2y^4)^5 is -243x^10y^20.

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