Решение:

1. a) $$ \frac{5a}{15b} = \frac{a}{3b} $$ б) $$ \frac{3c}{8c} = \frac{3}{8} $$ в) $$ \frac{b}{12b} = \frac{1}{12} $$ г) $$ \frac{-6}{18x} = \frac{-1}{3x} $$ д) $$ \frac{ac}{bc} = \frac{a}{b} $$ е) $$ \frac{xy}{2y} = \frac{x}{2} $$
2. a) $$ \frac{5a^2}{6a} = \frac{5a}{6} $$ б) $$ \frac{9b^4}{10b^3} = \frac{9b}{10} $$ в) $$ \frac{-5c^4}{10c^2} = \frac{-c^2}{2} $$ г) $$ \frac{3x^4}{x^3} = 3x $$ д) $$ \frac{12y^3}{-42y^5} = \frac{-2}{7y^2} $$ е) $$ \frac{21z^8}{39z} = \frac{7z^7}{13} $$
3. a) $$ \frac{a^2b^5}{ab^7} = \frac{a}{b^2} $$ б) $$ \frac{-63xy^5}{81xy^4} = \frac{-7y}{9} $$ в) $$ \frac{30a^2c^3}{48a^3c^2} = \frac{5c}{8a} $$ г) $$ \frac{111p^5q^6}{37p^4q^4} = 3pq^2 $$
4. a) $$(\frac{2}{5})^3 = \frac{8}{125} $$ б) $$(\frac{3}{4})^6 = \frac{729}{4096} $$ в) $$(\frac{7}{3})^3 = \frac{343}{27} $$ г) $$ \frac{625}{5^5} = \frac{5^4}{5^5} = \frac{1}{5} $$
5. a) $$ \frac{125^3}{25^4} = \frac{(5^3)^3}{(5^2)^4} = \frac{5^9}{5^8} = 5 $$ б) $$ \frac{64^5}{128^4} = \frac{(2^6)^5}{(2^7)^4} = \frac{2^{30}}{2^{28}} = 2^2 = 4 $$ в) $$ \frac{81^6}{27^8} = \frac{(3^4)^6}{(3^3)^8} = \frac{3^{24}}{3^{24}} = 1 $$
6. a) $$ \frac{x(a+3)}{y(a+3)} = \frac{x}{y} $$ б) $$ \frac{3(x+5)^2}{(x+5)^3} = \frac{3}{x+5} $$ в) $$ \frac{3a(b-2)}{6(b-2)^2} = \frac{a}{2(b-2)} $$ г) $$ \frac{x^2(x-8)^3}{x^4(x-8)^2} = \frac{x-8}{x^2} $$ д) $$ \frac{3a+3b}{5(a+b)} = \frac{3(a+b)}{5(a+b)} = \frac{3}{5} $$ е) $$ \frac{7x-14y}{3x-6y} = \frac{7(x-2y)}{3(x-2y)} = \frac{7}{3} $$