(3x4y2)4 Fully Simplified

less than a minute read Jun 16, 2024

Simplifying (3x⁴y²)⁴

This expression involves several concepts in algebra, namely:

Exponents: A number indicating how many times a base number is multiplied by itself.
Power of a product: This rule states that (ab)ⁿ = aⁿbⁿ
Power of a power: This rule states that (aⁿ)ᵐ = aⁿᵐ

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

First, we apply the power of a product rule to distribute the outer exponent (4) to each factor within the parentheses:

(3x⁴y²)⁴ = 3⁴ (x⁴)⁴ (y²)⁴

Next, we use the power of a power rule to simplify each factor:

3⁴ (x⁴)⁴ (y²)⁴ = 81 x¹⁶ y⁸

Therefore, the fully simplified form of (3x⁴y²)⁴ is 81x¹⁶y⁸.