1. The problem is to simplify the expression $y^3 + \frac{1}{x^3 y^3}$. 2. We start by recognizing the terms: the first term is $y^3$ and the second term is $\frac{1}{x^3 y^3}$. 3. There is no common factor to combine these terms directly, so the expression is already in its simplest form. 4. If desired, we can write the expression as a single fraction by finding a common denominator: $$y^3 = \frac{y^6 x^3}{x^3 y^3}$$ 5. Thus, $$y^3 + \frac{1}{x^3 y^3} = \frac{y^6 x^3}{x^3 y^3} + \frac{1}{x^3 y^3} = \frac{y^6 x^3 + 1}{x^3 y^3}$$ 6. This is a valid simplified form if a single fraction is preferred. Final answer: $$y^3 + \frac{1}{x^3 y^3} = \frac{y^6 x^3 + 1}{x^3 y^3}$$