Question

Помогите,срочно!Пожалуйста)​

Answer 1

1)

$1,6^{13}\cdot 0,625^{-14}=(\frac{16}{10})^{13}\cdot (\frac{625}{1000})^{-14}=(\frac{8}{5})^{13}\cdot (\frac{1000}{625})^{14}=(\frac{8}{5})^{13}\cdot(\frac{8}{5})^{14}=\\ \\ =(\frac{8}{5})^{(13+14)}=(\frac{8}{5})^{27}=1,6^{27}$

2)

$0,04^8\cdot 5^{15} =(\frac{4}{100})^8\cdot 5^{15}=(\frac{1}{25})^8\cdot 5^{15}=((\frac{1}{5})^2)^8\cdot 5^{15}=(5^{-2})^{8}\cdot 5^{15}=5^{-16}\cdot 5^{15}=\\\\=5^{(-16+15)}=5^{-1}=\frac{1}{5}=0,2$

3)

$\frac{0,01^2}{10^{-2}}\cdot 10^4=\frac{(\frac{1}{100})^2}{10^{-2}}\cdot 10^4=(10^{-2})^2\cdot 10^{2}\cdot 10^4=10^{-4}\cdot 10^2\cdot10^4=\\\\=10^{(-4+2+4)}=10^2=100$