Вычислите:
а) $\frac{2 * 3^{20} - 5 * 3^{19}}{9^9}$;
б) $\frac{(3 * 2^{20} + 7 * 2^{19}) * 52}{(13 * 8^4)^2}$;
в) $\frac{108 * 6^7 - 108 * 6^6}{216^3 - 36^4}$;
г) $\frac{(3^{15} + 3^{13}) * 2^9}{(3^{14} + 3^{12}) * 1024}$.
$\frac{2 * 3^{20} - 5 * 3^{19}}{9^9} = \frac{3^{19}(2 * 3 - 5)}{(3^2)^9} = \frac{3^{19}(6 - 5)}{3^{18}} = \frac{3^{19}}{3^{18}} = 3$
$\frac{(3 * 2^{20} + 7 * 2^{19}) * 52}{(13 * 8^4)^2} = \frac{(2^{19}(3 * 2 + 7)) * 52}{13^2 * 8^8} = \frac{(2^{19}(6 + 7)) * 13 * 4}{13^2 * (2^3)^8} = \frac{2^{19}(6 + 7) * 2^2}{13 * 2^{24}} = \frac{2^{21} * 13}{13 * 2^{24}} = \frac{1}{2^3} = \frac{1}{8}$
$\frac{108 * 6^7 - 108 * 6^6}{216^3 - 36^4} = \frac{108 * 6^6(6 - 1)}{(6^3)^3 - (6^2)^4} = \frac{3 * 36 * 6^6 * 5}{6^9 - 6^8} = \frac{3 * 6^2 * 6^6 * 5}{6^8(6 - 1)} = \frac{3 * 6^8 * 5}{6^8 * 5} = 3$
$\frac{(3^{15} + 3^{13}) * 2^9}{(3^{14} + 3^{12}) * 1024} = \frac{3^{13}(3^2 + 1) * 2^9}{3^{12}(3^2 + 1) * 2^{10}} = \frac{3}{2} = 1\frac{1}{2}$
Пожауйста, оцените решение
