Question

упростите выражение. ​

Answer 1

1)

$\frac{3^{5}+3^{9}}{3^{-5}+3^{-9}} =3^{5}(1+3^{4}) : (\frac{1}{3^{5}} +\frac{1}{3^{9}} )=3^{5}(1+3^{4}) : \frac{3^{4}+1}{3^{9}} =\frac{3^{5}(1+3^{4})*3^{9}}{1+3^{4}} =3^{14}$

2)

$\frac{2^{5}+2^{6}+2^{7}}{2^{-5}+2^{-6}+2^{-7}} =2^{5}(1+2+2^{2}):(\frac{1}{2^{5}} +\frac{1}{2^{6}} +\frac{1}{2^{7}} )=7*2^{5} :\frac{4+2+1}{2^{7}} =\frac{7*2^{5}*2^{7}}{7} =2^{12}$