1. The problem is to simplify each algebraic expression involving division of monomials and match the simplified form to the given answer choices. 2. The key rule is that when dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. Simplify each expression step-by-step: ① $$\frac{n^9}{n^5} = n^{9-5} = n^4$$ matches F. ② $$\frac{n^{12}}{n^3} = n^{12-3} = n^9$$ matches H. ③ $$\frac{2n^4}{n} = 2n^{4-1} = 2n^3$$ matches E. ④ $$\frac{6n^2}{3n^5} = \frac{6}{3} n^{2-5} = 2n^{-3} = \frac{2}{n^3}$$ matches Y. ⑤ $$\frac{x^3 y^4}{x^2 y} = x^{3-2} y^{4-1} = x y^3$$ matches A. ⑥ $$\frac{-8x^6 y^2}{2x^3 y^2} = \frac{-8}{2} x^{6-3} y^{2-2} = -4 x^3$$ matches R. ⑦ $$\frac{8 x y^2}{12 x^3 y^5} = \frac{8}{12} x^{1-3} y^{2-5} = \frac{2}{3} x^{-2} y^{-3} = \frac{2}{3 x^2 y^3}$$ matches E. ⑧ $$\frac{20 x^3 y^8}{-5 x^3 y} = \frac{20}{-5} x^{3-3} y^{8-1} = -4 y^7$$ matches T. ⑨ $$\frac{3 a^5 b^2}{9 a^2 b^5} = \frac{3}{9} a^{5-2} b^{2-5} = \frac{1}{3} a^3 b^{-3} = \frac{a^3}{3 b^3}$$ matches H. ⑩ $$\frac{-15 a^2 b^9}{-3 a b} = \frac{-15}{-3} a^{2-1} b^{9-1} = 5 a b^8$$ matches I. ⑪ $$\frac{-24 a^2 b}{18 a b^5} = \frac{-24}{18} a^{2-1} b^{1-5} = -\frac{4}{3} a b^{-4} = -\frac{4 a}{3 b^4}$$ matches N. ⑫ $$\frac{30 a^9 b^2}{2 a^6 b^2} = \frac{30}{2} a^{9-6} b^{2-2} = 15 a^3$$ matches G. ⑬ $$\frac{8 u^4 v^{10}}{-2 u^2 v^8} = \frac{8}{-2} u^{4-2} v^{10-8} = -4 u^2 v^2$$ matches S. ⑭ $$\frac{13 u^7 v^7}{26 u^7 v} = \frac{13}{26} u^{7-7} v^{7-1} = \frac{1}{2} v^6$$ matches T. ⑮ $$\frac{-7 u^2 v^6}{u v^3} = -7 u^{2-1} v^{6-3} = -7 u v^3$$ matches O. ⑯ $$\frac{-9 u^8 v^2}{-6 u^2 v^6} = \frac{-9}{-6} u^{8-2} v^{2-6} = \frac{3}{2} u^6 v^{-4} = \frac{3 u^6}{2 v^4}$$ matches A. ⑰ $$\frac{14 k^9 m^3}{2 k m^3} = \frac{14}{2} k^{9-1} m^{3-3} = 7 k^8$$ matches D. ⑱ $$\frac{4 k^2 m^2}{16 k^5 m^3} = \frac{4}{16} k^{2-5} m^{2-3} = \frac{1}{4} k^{-3} m^{-1} = \frac{1}{4 k^3 m}$$ matches O. ⑲ $$\frac{-3 k^5 m^6}{k^4 m^3} = -3 k^{5-4} m^{6-3} = -3 k m^3$$ matches R. ⑳ $$\frac{12 k m^3}{-4 m^3} = \frac{12}{-4} k m^{3-3} = -3 k$$ matches E. 4. Final answers for each exercise are: ① F ② H ③ E ④ Y ⑤ A ⑥ R ⑦ E ⑧ T ⑨ H ⑩ I ⑪ N ⑫ G ⑬ S ⑭ T ⑮ O ⑯ A ⑰ D ⑱ O ⑲ R ⑳ E This completes the simplification and matching process.