a)
[tex]5^8*(\frac1{25})^8:(\frac15)^5=5^8*(\frac1{5^2})^8:5^{-5}=5^8*5^{-16}:5^{-5}=5^{8+(-16)-(-5)}=5^{8-16+5}=5^{-3}=\frac1{5^3}=\frac1{125}[/tex]
b)
[tex]\frac{(\frac13)^8:(\frac5{12})^8}{0,8^6}=((\frac13)^8:(\frac5{12})^8):0,8^6=(\frac13:\frac5{12})^8:(\frac45)^6=(\frac13*\frac{12}5)^8:(\frac45)^6=(\frac{4}{5})^8:(\frac45)^6=(\frac45)^{8-6}=(\frac{4}{5})^2=\frac{4^2}{5^2}=\frac{16}{25}=\frac{64}{100}=0,64[/tex]
Wykorzystane zaleznosci:
[tex]a^{-n}=\frac1{a^n}\\a^n*a^m=a^{n+m}\\a^n:a^m=a^{n-m}\\a^n*b^n=(a*b)^n\\a^n:b^n=(a:b)^n\\[/tex]
