Question

Помогите, пожалуйста решить номера 5,6,7,8
Не могу сам справиться

Answer 1

$5)\frac{8^{5}+8^{4}}{4^{8}+4^{7}+4^{9}}=\frac{8^{4}(8+1) }{4^{7}(4+1+4^{2})}=\frac{8^{4}*9}{4^{7}*21}=\frac{(2^{3})^{4}*3}{(2^{2})^{7}*7}=\frac{2^{12}*3}{2^{14}*7}=\frac{3}{28}$

$6)\frac{27^{11}-27^{10}-27^{9}}{9^{15}-9^{14}-9^{13}}=\frac{27^{9}(27^{2}-27-1)}{9^{13}(9^{2}-9-1)}=\frac{27^{9}*701 }{9^{13}*71 }=\frac{(3^{3})^{9}*701}{(3^{2})^{13}*71}=\frac{3^{27}*701 }{3^{26}*71}=\frac{2103}{71}=29\frac{44}{71}$

$7)\frac{16^{7}-16^{5}}{8^{10}-8^{9}+8^{8}}=\frac{16^{5}(16^{2}-1)}{8^{8}(8^{2}-8+1)}=\frac{16^{5}*255}{8^{8}*57}=\frac{(2^{4})^{5}*255}{(2^{3})^{8}*57}=\frac{2^{20}*255 }{2^{24}*57}=\frac{255}{16*57}=\frac{255}{912}=\frac{85}{304}$

$\frac{9^{23}+9^{22}+9^{21}}{27^{14}-27^{13}}=\frac{9^{21}(9^{2}+9+1)}{27^{13}(27-1)}}=\frac{9^{21}*91 }{27^{13}*26}=\frac{(3^{2})^{21}*7}{(3^{3})^{13}*2}=\frac{3^{42}*7 }{3^{39}*2}=\frac{27*7}{2}=94,5$