1 вариант:
а)
![5^1*5^{-5}=5^{1+(-5)}=5^{-4}=\frac{1}{5^4}=\frac{1}{625}](https://tex.z-dn.net/?f=5%5E1%2A5%5E%7B-5%7D%3D5%5E%7B1%2B%28-5%29%7D%3D5%5E%7B-4%7D%3D%5Cfrac%7B1%7D%7B5%5E4%7D%3D%5Cfrac%7B1%7D%7B625%7D)
б)
![3*(\frac{1}{3})^{-2}=3^1*3^{-1*-2}=3^1*3^2=3^{1+2}=3^3=27](https://tex.z-dn.net/?f=3%2A%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B-2%7D%3D3%5E1%2A3%5E%7B-1%2A-2%7D%3D3%5E1%2A3%5E2%3D3%5E%7B1%2B2%7D%3D3%5E3%3D27)
в)
![\frac{4^{-3}*2^6}{8}=\frac{2^{2*-3}*2^6}{2^3}=2^{-6+6-3}=2^{-3}=\frac{1}{2^3}=\frac{1}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5E%7B-3%7D%2A2%5E6%7D%7B8%7D%3D%5Cfrac%7B2%5E%7B2%2A-3%7D%2A2%5E6%7D%7B2%5E3%7D%3D2%5E%7B-6%2B6-3%7D%3D2%5E%7B-3%7D%3D%5Cfrac%7B1%7D%7B2%5E3%7D%3D%5Cfrac%7B1%7D%7B8%7D)
2 вариант.
а)
![2^1*2^{-3}=2^{1-3}=2^{-2}=\frac{1}{4}](https://tex.z-dn.net/?f=2%5E1%2A2%5E%7B-3%7D%3D2%5E%7B1-3%7D%3D2%5E%7B-2%7D%3D%5Cfrac%7B1%7D%7B4%7D)
б)
![(\frac{1}{4})^{-2}*4=4^{-1*-2}*4^1=4^{2+1}=4^3=64](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B-2%7D%2A4%3D4%5E%7B-1%2A-2%7D%2A4%5E1%3D4%5E%7B2%2B1%7D%3D4%5E3%3D64)
в)
![\frac{((3)^{-2})^3*27^2}{3}=\frac{3^{-2*3}*3^{3*2}}{3}=\frac{3^{-6+6}}{3}=\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B%28%283%29%5E%7B-2%7D%29%5E3%2A27%5E2%7D%7B3%7D%3D%5Cfrac%7B3%5E%7B-2%2A3%7D%2A3%5E%7B3%2A2%7D%7D%7B3%7D%3D%5Cfrac%7B3%5E%7B-6%2B6%7D%7D%7B3%7D%3D%5Cfrac%7B1%7D%7B3%7D)
Качество фото не лучшее, поэтому мог записать некоторые примеры неправильно.
Решение
Cos(a-П) = cos(π - a) = - cosa
sin(a-П) = - sin(π - a) = - sina
tg(a-П) = - tg(π - a) = tga
Сумма бесконечно убывающей геометрической прогрессии:
S=16 / (1 - 3/4) = 16 / (1/4) = 16 * 4 = 64.