Question

Решите пример пожалуйста!

Answer 1

$1) frac{2^{19}*27^3+1*4^9*9^4}{6^9*2^{10}+12^{10}} = frac{2^{19}*3^9+2^{18}*3^8}{2^9*3^9*2^{10}+3^{10}*4^{10}} = frac{2^{19}*3^9+2^{18}*3^8}{3^9*2^{19}+3^{10}*2^{20}} = frac{2^{18}*3^8(2*3+1)}{3^9*2^{19}(1+3*2)} = \\ = frac{2^{18}*3^8*7}{3^9*2^{19}*7}=frac{1}{2*3} =frac{1}{6}$

$2) frac{5*4^{15}*9^9-4*3^{20}*8^9}{5*2^9*6^{19}-7*2^{29}*27^6}=frac{5*2^{30}*3^{18}-2^2*3^{20}*2^{27}}{5*2^9*3^{19}*2^{19}-7*2^{29}*3^{18}}=frac{5*2^{30}*3^{18}-3^{20}*2^{29}}{5*3^{19}*2^{28}-7*2^{29}*3^{18}}= \ \ =frac{2^{29}*3^{18}(5*2-3^{2})}{3^{18}*2^{28}(5*3-7*2)}=frac{2(10-9)}{(15-14)}=2$