(2x^2y^4)^5

Jasonbradley

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Jun 16, 2024

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Simplifying (2x²y⁴)⁵

This expression involves exponents and parentheses. To simplify it, we'll use the following rules:

• Power of a product: (ab)ⁿ = aⁿbⁿ
• Power of a power: (aⁿ)ᵐ = aⁿᵐ

Let's break down the simplification step-by-step:

1. Apply the power of a product rule:

(2x²y⁴)⁵ = 2⁵(x²)⁵(y⁴)⁵

2. Apply the power of a power rule:

2⁵(x²)⁵(y⁴)⁵ = 32x¹⁰y²⁰

Therefore, the simplified form of (2x²y⁴)⁵ is 32x¹⁰y²⁰.

Key Points:

• Exponents represent repeated multiplication: For example, x² = x * x.
• When multiplying powers with the same base, add the exponents: For example, x² * x³ = x⁵.
• When raising a power to another power, multiply the exponents: For example, (x²)³ = x⁶.