BRADZO PROSZĘ O POMOC   Zadania w załączniku   Z góry dziękuję ;)

Własności działań na potęgach: [latex]a^{n}*a^{m}=a^{n+m}\ a^{n}:a^{m}=a^{n-m}\ (a^{n})^{m}=a^{n*m}\ a^{-n}=(frac{1}{a})^{n}\ a^{n}*b^{n}=(ab)^{n} [/latex] ================================================================ zad 1 a) [latex]3sqrt{3^{2}}=3*(3^{2})^{frac{1}{2}}=3*3^{frac{1}{2}*2}=3*3=3^{2}=9[/latex] --------------------------------------------------------------- b) [latex]sqrt[3]{7^{-5}}=(7^{-5})^{frac{1}{3}}=7^{-5*frac{1}{3}}=7^{-frac{5}{3}}=frac{1}{7}^{frac{5}{3}}[/latex] ================================ zad 2 [latex]frac{(5^{2}-2^{2})(5^{frac{1}{3}}-2^{frac{1}{3}})}{5^{frac{4}{3}}+2*5^{frac{1}{3}}-5*2^{frac{1}{3}}-2^{frac{4}{3}}}=frac{(5^{2}-2^{2})(5^{frac{1}{3}}-2^{frac{1}{3}})}{5*5^{frac{1}{3}}+2*5^{frac{1}{3}}-5*2^{frac{1}{3}}-2*2^{frac{1}{3}}}=\[/latex] [latex]=frac{(5^{2}-2^{2})(5^{frac{1}{3}}-2^{frac{1}{3}})}{5^{frac{1}{3}}(5+2)-2^{frac{1}{3}}(5+2)}=frac{(5^{2}-2^{2})(5^{frac{1}{3}}-2^{frac{1}{3}})}{7*(5^{frac{1}{3}}-2^{frac{1}{3}})}=frac{25-4}{7}=frac{21}{7}=3[/latex] ================================ zad 3 a)  [latex]frac{(11^{frac{1}{2}}-2^{frac{1}{2}})(sqrt{11}+sqrt{2})}{(sqrt[3]{125}-sqrt[3]{8})^{2}}=frac{(11^{frac{1}{2}}-2^{frac{1}{2}})(11^{frac{1}{2}}+2^{frac{1}{2}})}{(sqrt[3]{5^{3}}-sqrt[3]{2^{3}})^{2}}=frac{(11^{frac{1}{2}})^{2}-(2^{frac{1}{2}})^{2}}{(5-2)^{2}}=\ =frac{11-2}{3^{2}}=frac{9}{9}=1[/latex] --------------------------------------------------------------- b) [latex]frac{(4*7^{frac{1}{2}}+4*2^{frac{1}{2}})^{2}}{18+2*56^{frac{1}{2}}}=frac{4^{2}(sqrt{7}+sqrt{2})^{2}}{2(9+sqrt{56})}=frac{16*(7+2sqrt{14}+2)}{2*(9+2sqrt{14})}=\ =8[/latex] ================================ zad 4 [latex](frac{asqrt{a}*bsqrt[3]{b}}{sqrt[3]a^{2}*sqrt{b}})^{0,6}=(frac{a*a^{frac{1}{2}}*b*b^{frac{1}{3}}}{a^{frac{2}{3}}*b^{frac{1}{2}}})^{frac{3}{5}}=\ =(frac{a^{frac{3}{2}}*b^{frac{4}{3}}}{a^{frac{2}{3}}*b^{frac{1}{2}}})^{frac{3}{5}}=(a^{frac{5}{6}}*b^{frac{5}{6}})^{frac{3}{5}}=\ [/latex] [latex]=[(ab)^{frac{5}{6}}]^{frac{3}{5}}=(ab)^{frac{5}{6}*frac{3}{5}}=(ab)^{frac{1}{2}}=sqrt{ab}[/latex] ================================ zad 5 a)  [latex]128^{frac{2}{10}}=(2^{7})^{frac{1}{5}}=2^{frac{7}{5}}\ sqrt[5]{64}=(2^{6})^{frac{1}{5}}=2^{frac{6}{5}}\ 128^{frac{2}{10}}>sqrt[5]{64}[/latex] --------------------------------------------------------------- b)  [latex]sqrt[7]{36}=(6^{2})^{frac{1}{7}}=6^{frac{2}{7}}\ (6^{frac{1}{14}})^{2}=6^{frac{1}{7}}\ sqrt[7]{36}>(6^{frac{1}{14}})^{2}[/latex]  

Zadanie do wglądu w załączniku.   /mialem problemy z odczytem niektorych liczb, ale mam nadzieję że dobrze odczytałem