Question

2.19. Упростите выражение:​

Answer 1

$1) \ \dfrac{3^{5}+3^{9}}{3^{-5}+3^{-9}} =\dfrac{3^{5}(1+3^{4})}{3^{-9}(3^{4}+1)} =\dfrac{3^{5} }{3^{-9} }=3^{5-(-9)}=3^{5+9} =3^{14}=\boxed{4782969}\\\\\\2) \ \dfrac{2^{5} +2^{6}+2^{7}}{2^{-5}+2^{-6}+2^{-7}} =\dfrac{2^{5}(1 +2+2^{2})}{2^{-7}(2^{2} +2+1)} =\dfrac{2^{5} }{2^{-7} }=2^{5-(-7)}=\\\\\\=2^{5+7} =2^{12}=\boxed{4096}$

Answer 2

Ответ:

Объяснение:

$\displaystyle\bf\\1)\ \frac{3^5+3^9}{3^{-5}+3^{-9}} =\frac{3^5+3^9}{\dfrac{1}{3^5}+\dfrac{1}{3^9} } =\frac{3^5+3^9}{\dfrac{3^9+3^5}{3^5\cdot3^9} }=\frac{(3^5+3^9)\cdot3^{5+9}}{(3^5+3^9)} =3^{14}$

$\displaystyle\bf\\2)\ \frac{2^5+2^6+2^7}{2^{-5}+2^{-6}+2^{-7}} =\frac{2^5+2^6+2^7}{\dfrac{1}{2^5} +\dfrac{1}{2^6} +\dfrac{1}{2^7} } =\frac{2^5+2^6+2^7}{\dfrac{2^7+2^6+2^5}{2^{12}} } =2^{12}$