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(3x^4y)^3

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

Simplifying (3x^4y)^3

This article will guide you through simplifying the expression (3x^4y)^3. We will utilize the rules of exponents to achieve a simplified form.

Understanding the Exponent Rules

Before we tackle the simplification, let's refresh our memory on the key exponent rules we'll be using:

  • Power of a product: (ab)^n = a^n * b^n
  • Power of a power: (a^m)^n = a^(m*n)

Simplifying the Expression

  1. Apply the power of a product rule: (3x^4y)^3 = 3^3 * (x^4)^3 * y^3

  2. Apply the power of a power rule: 3^3 * (x^4)^3 * y^3 = 27 * x^(4*3) * y^3

  3. Simplify the exponents: 27 * x^(4*3) * y^3 = 27x^12y^3

Conclusion

Therefore, the simplified form of (3x^4y)^3 is 27x^12y^3. By applying the rules of exponents, we were able to break down the expression and arrive at a simplified result. Remember, understanding these rules is crucial for successfully manipulating expressions involving exponents.

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