(3x^3y^2)^3

Jasonbradley

2 min read

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Jun 16, 2024

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Simplifying (3x^3y^2)^3

In mathematics, simplifying expressions is a crucial step in solving equations and understanding relationships between variables. Let's break down how to simplify the expression (3x^3y^2)^3.

Understanding the Properties

We'll use two fundamental properties of exponents:

1. Power of a Product: (ab)^n = a^n * b^n
2. Power of a Power: (a^m)^n = a^(m*n)

Step-by-Step Simplification

1. Apply the Power of a Product Property: (3x^3y^2)^3 = 3^3 * (x^3)^3 * (y^2)^3

2. Apply the Power of a Power Property: 3^3 * (x^3)^3 * (y^2)^3 = 27 * x^(33) * y^(23)

3. Simplify the exponents: 27 * x^(33) * y^(23) = 27x^9y^6

Conclusion

The simplified form of (3x^3y^2)^3 is 27x^9y^6. This process demonstrates the power of applying exponent properties to manipulate and simplify complex expressions.