550. Найдите значение выражения: a) $$13^{100}: 13^{98}$$; б) $$3^{8} \cdot 2^{7} : 3^{6} \cdot 2^{5}$$; в) $$2^{14}: 8^{4}$$; г) $$9^{5} \cdot 5^{9} : 3^{9} \cdot 5^{10}$$; д) $$5^{10}: 25^{4}$$; е) $$\frac{3^{8} \cdot 5^{8}}{3^{10} \cdot 5^{7}}$$; ж) $$\frac{2^{4}6}{2^{8} \cdot 3^{5}}$$; 3) $$\frac{2^{7} \cdot 3^{6} \cdot 5^{5}}{12^{3}}$$.

**a) $$13^{100}: 13^{98}$$** $$13^{100}: 13^{98} = 13^{100-98} = 13^2 = 169$$ **б) $$3^{8} \cdot 2^{7} : 3^{6} \cdot 2^{5}$$** $$3^{8} \cdot 2^{7} : 3^{6} \cdot 2^{5} = \frac{3^8 \cdot 2^7}{3^6 \cdot 2^5} = 3^{8-6} \cdot 2^{7-5} = 3^2 \cdot 2^2 = 9 \cdot 4 = 36$$ **в) $$2^{14}: 8^{4}$$** $$2^{14}: 8^{4} = 2^{14}: (2^3)^4 = 2^{14}: 2^{12} = 2^{14-12} = 2^2 = 4$$ **г) $$9^{5} \cdot 5^{9} : 3^{9} \cdot 5^{10}$$** $$9^{5} \cdot 5^{9} : 3^{9} \cdot 5^{10} = \frac{9^5 \cdot 5^9}{3^9 \cdot 5^{10}} = \frac{(3^2)^5 \cdot 5^9}{3^9 \cdot 5^{10}} = \frac{3^{10} \cdot 5^9}{3^9 \cdot 5^{10}} = 3^{10-9} \cdot 5^{9-10} = 3^1 \cdot 5^{-1} = \frac{3}{5} = 0.6$$ **д) $$5^{10}: 25^{4}$$** $$5^{10}: 25^{4} = 5^{10}: (5^2)^4 = 5^{10}: 5^8 = 5^{10-8} = 5^2 = 25$$ **e) $$\frac{3^{8} \cdot 5^{8}}{3^{10} \cdot 5^{7}}$$** $$\frac{3^{8} \cdot 5^{8}}{3^{10} \cdot 5^{7}} = 3^{8-10} \cdot 5^{8-7} = 3^{-2} \cdot 5^1 = \frac{1}{3^2} \cdot 5 = \frac{5}{9}$$ **ж) $$\frac{2^{4} \cdot 6}{2^{8} \cdot 3^{5}}$$** $$\frac{2^{4} \cdot 6}{2^{8} \cdot 3^{5}} = \frac{2^4 \cdot 2 \cdot 3}{2^8 \cdot 3^5} = \frac{2^5 \cdot 3}{2^8 \cdot 3^5} = 2^{5-8} \cdot 3^{1-5} = 2^{-3} \cdot 3^{-4} = \frac{1}{2^3 \cdot 3^4} = \frac{1}{8 \cdot 81} = \frac{1}{648}$$ **3) $$\frac{2^{7} \cdot 3^{6} \cdot 5^{5}}{12^{3}}$$** $$\frac{2^{7} \cdot 3^{6} \cdot 5^{5}}{12^{3}} = \frac{2^{7} \cdot 3^{6} \cdot 5^{5}}{(2^2 \cdot 3)^3} = \frac{2^{7} \cdot 3^{6} \cdot 5^{5}}{2^6 \cdot 3^3} = 2^{7-6} \cdot 3^{6-3} \cdot 5^5 = 2^1 \cdot 3^3 \cdot 5^5 = 2 \cdot 27 \cdot 3125 = 54 \cdot 3125 = 16875$$