Question

3^5+3^9 /3^-5+3^-9 и 2^5+2^6+2^7 / 2^-5+2^-6+2^-7

Answer 1

$\frac{3^5+3^9}{3^{-5}+3^{-9}} = \frac{3^5+3^9}{\frac{1}{3^5}+\frac{1}{3^9} }= \frac{3^5+3^9}{\frac{3^9+3^5}{3^5\cdot 3^9}} =3^5\cdot 3^9=3^{14}\\\\\\ \frac{2^5+2^6+2^7}{2^{-5}+2^{-6}+2^{-7}} = \frac{2^5+2^6+2^7}{\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7} } = \frac{2^5+2^6+2^7}{ \frac{2^6\cdot 2^7+2^5\cdot 2^7+2^5\cdot 2^6}{2^5\cdot 2^6\cdot 2^7} } =\\\\= \frac{(2^5+2^6+2^7)\cdot 2^{18}}{2^{13}+2^{12}+2^{11}} = \frac{(2^5+2^6+2^7)\cdot 2^{18}}{2^{11}\cdot (2^2+2+1)} = \frac{(2^5+2^6+2^7)\cdot 2^{7}}{4+2+1}$

$= \frac{2^5\cdot (1+2+2^2)\cdot 2^7}{7} = \frac{2^5\cdot 7\cdot 2^7}{7} =2^5\cdot 2^7=2^{12}$