usun niewymiernosc z mianownika [latex] frac{3 sqrt{5} - sqrt{2} }{ sqrt{5} - sqrt{2} } =[/latex] oblicz: [latex] 5^{-3}*125 ^{ frac{2}{3} } *625 ^{ frac{5}{4} }= [/latex] [latex]2^{} :16 ^{- frac{3}{2} }*32 ^{1,2} =[/latex]

[latex] frac{3sqrt5-sqrt2}{sqrt5-sqrt2}* frac{sqrt5+sqrt2}{sqrt5+sqrt2}= frac{3sqrt5*sqrt5+3sqrt5*sqrt2-sqrt2*sqrt5-sqrt2*sqrt2}{sqrt5^2-sqrt2^2}=\\= frac{3*5+3sqrt{10}-sqrt{10}-2}{5-2}= frac{15-2+2sqrt{10}}{3} = frac{13+2sqrt{10}}{3} [/latex] [latex]oblicz:\1)\...=5^{-3}*(5^3)^{frac{2}{3}}*(5^4)^{frac{5}{4}}=5^{-3}*5^2*5^5=5^{-3+2+5}=5^4=625\\2)\...=2:(2^4)^{-frac{3}{2}}*(2^5)^{1,2}=2:2^{-6}*2^6=2^{1-(-6)+6}=2^{13}=8192[/latex]