(3x^2y^3)^3 Simplify

Jasonbradley

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Jun 16, 2024

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

This expression involves simplifying a term raised to a power. We'll use the rules of exponents to solve this problem.

Understanding the Rules

• 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^2y^3)^3 = 3^3 * (x^2)^3 * (y^3)^3

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

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

Therefore, the simplified form of (3x^2y^3)^3 is 27x^6y^9.