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(27x^6y^12)^1/3

2 min read Jun 16, 2024
(27x^6y^12)^1/3

Simplifying the Expression (27x^6y^12)^1/3

This article will explore the simplification of the expression (27x^6y^12)^1/3. We'll break down the process step-by-step and explain the underlying mathematical principles.

Understanding the Properties of Exponents

The key to simplifying this expression lies in understanding the properties of exponents. Here are some important rules:

  • Product of Powers: (a^m)^n = a^(m*n)
  • Power of a Product: (ab)^n = a^n * b^n

Applying the Properties to Simplify

  1. Apply the Power of a Product Rule:
    (27x^6y^12)^1/3 = 27^(1/3) * (x^6)^(1/3) * (y^12)^(1/3)

  2. Apply the Product of Powers Rule: 27^(1/3) * (x^6)^(1/3) * (y^12)^(1/3) = 27^(1/3) * x^(6/3) * y^(12/3)

  3. Simplify the Exponents: 27^(1/3) * x^(6/3) * y^(12/3) = 3 * x^2 * y^4

Conclusion

Therefore, the simplified form of (27x^6y^12)^1/3 is 3x^2y^4. This process demonstrates how applying the properties of exponents can effectively simplify complex expressions.

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