1. **State the problem:** Simplify the expression $$\frac{5x^7 y^7}{25x^7 y^2}$$. 2. **Recall the rules:** - When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. - You can simplify coefficients by dividing them. 3. **Simplify the coefficients:** $$\frac{5}{25} = \frac{\cancel{5}^1}{\cancel{5}^5} = \frac{1}{5}$$ 4. **Simplify the $x$ terms:** $$\frac{x^7}{x^7} = x^{7-7} = x^0 = 1$$ 5. **Simplify the $y$ terms:** $$\frac{y^7}{y^2} = y^{7-2} = y^5$$ 6. **Combine all simplified parts:** $$\frac{1}{5} \times 1 \times y^5 = \frac{y^5}{5}$$ **Final answer:** $$\frac{y^5}{5}$$