1.) Przedstaw w postaci potęgi liczby 3 pierwiastki; a) sqrt[3]{3 sqrt{3} } b) sqrt[4]{27*3 ^{-3} } c) sqrt[4]{3 sqrt{3} ^{-2} } d) sqrt[5]{9 sqrt{9} ^{-3} } 2.) Oblicz sumę liczb (-3) i 12 powiększoną o iloraz liczb frac{1}{2} i 4 3.) Oblicz

Zadanie 1 [latex]a) sqrt[3]{3 sqrt{3} } =left(3sqrt{3} ight) ^{frac{1}{3}}=left(3cdot 3^{frac{1}{2}} ight) ^{frac{1}{3}}=left(3^{left(frac{3}{2} ight)} ight)^{frac{1}{3}}=3^{frac{1}{2}}[/latex] [latex]b) sqrt[4]{27cdot3 ^{-3} } =left( 3^3cdot3^{-3} ight)^{frac{1}{4}}=1^{frac{1}{4}}=1=3^0[/latex] [latex]c) sqrt[4]{3 sqrt{3} ^{-2} } =left( 3cdot3^{-frac{2}{2}} ight)^{frac{1}{4}}=left(3cdot3^{-1} ight)^{frac{1}{4}}=left(1 ight)^{frac{1}{4}}=1=3^0[/latex] [latex]d)sqrt[5]{9 sqrt{9} ^{-3} } =left( 9cdot9^{-frac{3}{2}} ight)^{frac{1}{5}}=left(9^{-frac{1}{2} ight) ^frac{1}{5}=9^{-frac{1}{10}}=3^{-frac{1}{5}[/latex] Zadanie 2 [latex]-3+left(12+frac{left( frac{1}{2} ight)}{4} ight)=-3+left(12+frac{1}{8} ight)=9frac{1}{8}[/latex] Zadanie 3 [latex]3frac{1}{5} - left(4-left(4cdot frac{8}{10} ight) ight)=3frac{1}{5} - left(4-frac{16}{5} ight)=3frac{1}{5} - left(4-3frac{1}{5} ight)=\=3frac{1}{5} - 4+3frac{1}{5} =-4[/latex]