## Simplifying the Expression: (x³y³ - 1/2x²y³ - x³y²) * (1/3x²y²)

Let's break down the simplification of the expression: (x³y³ - 1/2x²y³ - x³y²) * (1/3x²y²).

### Understanding the Expression

The expression is a product of two terms:

**(x³y³ - 1/2x²y³ - x³y²)**: This is a trinomial with terms containing variables 'x' and 'y' raised to different powers.**(1/3x²y²)**: This is a monomial, a single term with variables 'x' and 'y' raised to certain powers.

### Simplifying the Expression

To simplify the expression, we need to distribute the monomial (1/3x²y²) across the trinomial. This means multiplying each term in the trinomial by the monomial:

(1/3x²y²) * (x³y³) - (1/3x²y²) * (1/2x²y³) - (1/3x²y²) * (x³y²)

Now, let's simplify each term using the rules of exponents:

**(1/3x²y²) * (x³y³) = (1/3) * x² * x³ * y² * y³ = (1/3)x⁵y⁵****(1/3x²y²) * (1/2x²y³) = (1/3) * (1/2) * x² * x² * y² * y³ = (1/6)x⁴y⁵****(1/3x²y²) * (x³y²) = (1/3) * x² * x³ * y² * y² = (1/3)x⁵y⁴**

Therefore, the simplified expression is:

**(1/3)x⁵y⁵ - (1/6)x⁴y⁵ - (1/3)x⁵y⁴**

### Final Thoughts

By applying the distributive property and the rules of exponents, we successfully simplified the given expression. This process demonstrates how to effectively work with polynomial expressions involving multiplication and combining like terms.