(6x^4y^4)^3

Jasonbradley

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Jun 16, 2024

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Simplifying (6x⁴y⁴)³

In mathematics, simplifying expressions involves rewriting them in a more compact and understandable form. Let's break down how to simplify the expression (6x⁴y⁴)³.

Understanding the Concepts

• Exponents: An exponent indicates the number of times a base is multiplied by itself. In (6x⁴y⁴)³, the exponent 3 tells us to multiply the base (6x⁴y⁴) by itself three times.
• Power of a Product: When a product is raised to a power, each factor within the product is raised to that power. This means (ab)ⁿ = aⁿbⁿ.
• Power of a Power: When a power is raised to another power, the exponents are multiplied. This means (aⁿ)ᵐ = aⁿᵐ.

Applying the Rules

1. Distribute the exponent: Using the Power of a Product rule, we can distribute the exponent 3 to each factor within the parentheses:

   (6x⁴y⁴)³ = 6³ (x⁴)³ (y⁴)³

2. Simplify the exponents: Applying the Power of a Power rule, we multiply the exponents:

   6³ (x⁴)³ (y⁴)³ = 6³ x¹² y¹²

3. Calculate the constant: 6³ = 6 * 6 * 6 = 216

   216 x¹² y¹²

Final Result

Therefore, the simplified form of (6x⁴y⁴)³ is 216x¹²y¹².