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

Jasonbradley

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Jun 16, 2024

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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.