(6x^4y^6)^3

2 min read Jun 16, 2024
(6x^4y^6)^3

Simplifying the Expression (6x⁴y⁶)³

This article will guide you through the process of simplifying the expression (6x⁴y⁶)³.

Understanding the Concept

The expression (6x⁴y⁶)³ signifies that the entire term inside the parentheses, 6x⁴y⁶, is being multiplied by itself three times. This is a case of applying the power of a product rule in algebra, which states:

(ab)ⁿ = aⁿbⁿ

Applying the Rule

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

  1. Apply the power of a product rule: (6x⁴y⁶)³ = 6³(x⁴)³(y⁶)³

  2. Simplify each term: 6³ = 216 (x⁴)³ = x¹² (remember, when raising a power to another power, you multiply the exponents) (y⁶)³ = y¹⁸

  3. Combine the simplified terms: 216x¹²y¹⁸

Final Result

Therefore, the simplified form of (6x⁴y⁶)³ is 216x¹²y¹⁸.

Key Takeaways

  • The power of a product rule is essential for simplifying expressions with multiple terms raised to a power.
  • Remember to apply the power to each individual term within the parentheses.
  • Multiply exponents when raising a power to another power.

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