Zadanie 1 :
[tex](\frac{3}{7})^{-2}:(\frac{9}{49})^{-2}=(\frac{3}{7}\cdot\frac{49}{9})^{-2}=(\frac{7}{3})^{-2}=(\frac{3}{7})^2=\frac{9}{49}\\\\\frac{(3^5)^2\cdot(3^7\cdot3^0)}{3^2}=\frac{3^{10}:3^7}{3^2}=\frac{3^3}{3^2}=3\\\\(\frac{2}{3}+(\frac{2}{3})^{-2})^0=1\\\\\frac{3^2\cdot(3^3)^2}{3^5}=\frac{3^2\cdot3^6}{3^5}=\frac{3^8}{3^5}=3^3=27[/tex]
Zadanie 2 :
Podpunkt a)
[tex]\log_22^{-3}=-3[/tex]
Podpunkt b)
[tex]\log_\frac{1}{4}8=x\\\\(\frac{1}{4})^x=8\\\\((\frac{1}{2})^2)^x=(\frac{1}{2})^{-3}\\\\2x=-3 \ \ |:2\\\\x=-1,5\\\\\log_\frac{1}{4}8=-1,5[/tex]
