1. **State the problem:** Simplify the expression $$\frac{50x^6 y^2}{30x^3 y^5}$$. 2. **Recall the rules:** - When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. - Simplify coefficients by dividing their greatest common divisor. 3. **Simplify the coefficients:** $$\frac{50}{30} = \frac{\cancel{50}^{\times 5}}{\cancel{30}^{\times 3}} = \frac{5}{3}$$ 4. **Simplify the powers of $x$:** $$\frac{x^6}{x^3} = x^{6-3} = x^3$$ 5. **Simplify the powers of $y$:** $$\frac{y^2}{y^5} = y^{2-5} = y^{-3} = \frac{1}{y^3}$$ 6. **Combine all parts:** $$\frac{5}{3} \times x^3 \times \frac{1}{y^3} = \frac{5x^3}{3y^3}$$ **Final answer:** $$\frac{5x^3}{3y^3}$$