(5x^2y^4)^5

Jasonbradley

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Jun 16, 2024

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Simplifying (5x²y⁴)⁵

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

Understanding the Power of a Product Rule

The core principle we use here is the power of a product rule: (ab)ⁿ = aⁿbⁿ. This rule states that when raising a product to a power, we raise each factor in the product to that power.

Applying the Rule

1. Apply the power of a product rule: (5x²y⁴)⁵ = 5⁵ (x²)⁵ (y⁴)⁵

2. Simplify each factor:

   • 5⁵ = 3125
   • (x²)⁵ = x¹⁰ (using the power of a power rule: (aᵐ)ⁿ = aᵐⁿ)
   • (y⁴)⁵ = y²⁰

3. Combine the simplified factors: 3125x¹⁰y²⁰

Final Result

Therefore, the simplified form of (5x²y⁴)⁵ is 3125x¹⁰y²⁰.