1. **State the problem:** Given the system of equations $$x^2 y^3 = 10$$ and $$x^3 y^2 = 8$$, find the value of $$x^5 y^5$$. 2. **Understand the goal:** We want to find $$x^5 y^5$$, which can be rewritten as $$(x^5)(y^5) = (x y)^5$$ if we factor it, but since we don't know $$x y$$ directly, we will use the given equations to find $$x$$ and $$y$$ or their powers. 3. **Use the given equations:** - Equation 1: $$x^2 y^3 = 10$$ - Equation 2: $$x^3 y^2 = 8$$ 4. **Multiply the two equations:** $$ (x^2 y^3)(x^3 y^2) = 10 \times 8 $$ $$ x^{2+3} y^{3+2} = 80 $$ $$ x^5 y^5 = 80 $$ 5. **Conclusion:** The value of $$x^5 y^5$$ is $$80$$. **Final answer:** D) 80