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

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

Simplify the exponents: Applying the Power of a Power rule, we multiply the exponents:
6³ (x⁴)³ (y⁴)³ = 6³ x¹² y¹²

Calculate the constant: 6³ = 6 * 6 * 6 = 216
216 x¹² y¹²
Final Result
Therefore, the simplified form of (6x⁴y⁴)³ is 216x¹²y¹².