Obliczenia
[tex](1,1)^5:(1,1)^3=(1,1)^{5-3}=(1,1)^2=1,1\cdot1,1=1,21\\\\(\frac{3}{5})^4\cdot5^4=(\frac{3}{5}\cdot5)^4=3^4=3\cdot3\cdot3\cdot3=81\\\\(\frac{3}{5})^4\cdot(1\frac{2}{3})^5=(\frac{3}{5})^4\cdot(\frac{5}{3})^5=(\frac{3}{5})^4\cdot((\frac{3}{5})^{-1})^5=(\frac{3}{5})^4\cdot(\frac{3}{5})^{-5}=(\frac{3}{5})^{4+(-5)}=\\\\=(\frac{3}{5})^{4-5}=(\frac{3}{5})^{-1}=\frac{5}{3}=1\frac{2}{3}\\\\\frac{25^2\cdot5^3}{5^6}=\frac{(5^2)^2\cdot5^3}{5^6}=\frac{5^{2\cdot2}\cdot5^3}{5^6}=\frac{5^4\cdot5^3}{5^6}=\frac{5^7}{5^6}=5[/tex]
Wykorzystane wzory
[tex]a^m:a^n=a^{m-n}\\\\a^m\cdot a^n=a^{m+n}\\\\a^m\cdot b^m=(a\cdot b)^m\\\\a^{-1}=\frac{1}{a} \ (a\neq0)[/tex]
