3. Найдите значение выражения, используя свойства степеней: 1) a) $$2^3 \cdot (2^2)^3 : 2^{13}$$; б) $$5^{21} : (5^6)^2 : 5^7$$; 2) a) $$\frac{4^2}{2^3}$$; б) $$\frac{16^2}{4^3}$$; в) $$\frac{4^3 \cdot 4^4}{8^4}$$; 3) a) $$\frac{4^7 \cdot 8^7}{32^5}$$; б) $$\frac{12^{19}}{21^7 \cdot 6^{17}}$$; в) $$\frac{12^3}{2^3 \cdot 6^3}$$.

1) a) $$2^3 \cdot (2^2)^3 : 2^{13} = 2^3 \cdot 2^{2\cdot3} : 2^{13} = 2^3 \cdot 2^6 : 2^{13} = 2^{3+6} : 2^{13} = 2^9 : 2^{13} = 2^{9-13} = 2^{-4} = \frac{1}{2^4} = \frac{1}{16}$$ б) $$5^{21} : (5^6)^2 : 5^7 = 5^{21} : 5^{6\cdot2} : 5^7 = 5^{21} : 5^{12} : 5^7 = 5^{21-12} : 5^7 = 5^9 : 5^7 = 5^{9-7} = 5^2 = 25$$ 2) a) $$\frac{4^2}{2^3} = \frac{(2^2)^2}{2^3} = \frac{2^{2\cdot2}}{2^3} = \frac{2^4}{2^3} = 2^{4-3} = 2^1 = 2$$ б) $$\frac{16^2}{4^3} = \frac{(4^2)^2}{4^3} = \frac{4^{2\cdot2}}{4^3} = \frac{4^4}{4^3} = 4^{4-3} = 4^1 = 4$$ в) $$\frac{4^3 \cdot 4^4}{8^4} = \frac{4^{3+4}}{8^4} = \frac{4^7}{8^4} = \frac{(2^2)^7}{(2^3)^4} = \frac{2^{2\cdot7}}{2^{3\cdot4}} = \frac{2^{14}}{2^{12}} = 2^{14-12} = 2^2 = 4$$ 3) a) $$\frac{4^7 \cdot 8^7}{32^5} = \frac{(4 \cdot 8)^7}{32^5} = \frac{32^7}{32^5} = 32^{7-5} = 32^2 = (2^5)^2 = 2^{5\cdot2} = 2^{10} = 1024$$ б) $$\frac{12^{19}}{2^{17} \cdot 6^{17}} = \frac{12^{19}}{(2 \cdot 6)^{17}} = \frac{12^{19}}{12^{17}} = 12^{19-17} = 12^2 = 144$$ в) $$\frac{12^3}{2^3 \cdot 6^3} = \frac{12^3}{(2 \cdot 6)^3} = \frac{12^3}{12^3} = 1$$