[tex]5^7*( \frac{1}{5})^8= 5^7*(5^{-1})^8 =5^7*5^{(-1)*8}=5^7*5^{-8}=5^{7+(-8)}=5^{-1}=\frac{1}{5}\\\\ stosujemy\ dzialania\ na\ potegach :\\\\1)\\\\ \frac{1}{a^n} =a^{-n}\\\\ czyli :\\\\ \frac{1}{5} = 5^{-1} \\\\2)\\\\ (a^n)^m=a^{n*m}\\\\(5^{-1})^8=5^{(-1)*8}=5^{-8} \\\\ 3)\\\\a^n*a^m=a^{n+m}\\\\5^7*5^{-8}=5^{7+(-8)}=5^{-1}\\\\4)\\\\a^{-n}= \frac{1}{a^n}\\\\5^{-1}=\frac{1}{5^1}=\frac{1}{5}[/tex]
