Zadania w załączniku mega proszę o pomoc ponieważ tego nie rozumie DAJE NAJLEPSZĄ ODPOWIEDŹ ZADANIE 3 i 4

zad 3 [latex]a) 3^{frac{5}{4}}*3^{frac{3}{4}}=3^{frac{5}{4}+frac{3}{4}}=3^{frac{8}{4}}=3^{2}=9\ \ b) 5^{-frac{5}{4}}*5^{frac{4}{3}}=5^{-frac{5}{4}+frac{4}{3}}=5^{-frac{15}{12}+frac{16}{12}}=5^{frac{1}{12}}=sqrt[12]{5}\ \ c) 81^{frac{3}{4}}:81^{frac{1}{2}}=81^{frac{3}{4}-frac{1}{2}}=81^{frac{3}{4}-frac{2}{4}}=81^{frac{1}{4}}=(3^{4})^{frac{1}{4}}=3^{4*frac{1}{4}}=3^{1}=3[/latex] [latex]d) 9^{frac{1}{3}}:9^{-frac{1}{6}}=9^{frac{1}{3}-(-frac{1}{6})}=9^{frac{2}{6}+frac{1}{3}}=9^{frac{3}{6}}=9^{frac{1}{2}}=(3^{2})^{frac{1}{2}}=\ \ =3^{2*frac{1}{2}}=3^{1}=3\ \ e) 2^{frac{2}{5}}*8^{frac{1}{5}}=2^{frac{2}{5}}*(2^{3})^{frac{1}{5}}=2^{frac{2}{5}}*2^{3*frac{1}{5}}=2^{frac{2}{5}}*2^{frac{3}{5}}=\ \ =2^{frac{2}{5}+frac{3}{5}}=2^{frac{5}{5}}=2^{1}=2[/latex] [latex]f) 5^{-frac{2}{7}}:25^{-frac{1}{7}}=5^{-frac{2}{7}}:(5^{2})^{-frac{1}{7}}= 5^{-frac{2}{7}}:5^{2*(-frac{1}{7})}=5^{-frac{2}{7}}:5^{-frac{2}{7}}=\ \ =5^{-frac{2}{7}-(-frac{2}{7})}=5^{-frac{2}{7}+frac{2}{7}}=5^{0}=1\ \ g) 4^{frac{1}{3}}*16^{frac{1}{3}}=4^{frac{1}{3}}*(4^{2})^{frac{1}{3}}=4^{frac{1}{3}}*4^{2*frac{1}{3}}=4^{frac{1}{3}}*4^{frac{2}{3}}=\ \ =4^{frac{1}{3}+frac{2}{3}}=4^{1}=4\ [/latex] [latex]h) 9^{frac{3}{10}}:27^{-frac{4}{5}}=(3^{2})^{frac{3}{10}}:(3^{3})^{-frac{4}{5}}= 3^{2*frac{3}{10}}:3^{3*(-frac{4}{5})}=3^{frac{3}{5}}:3^{-frac{12}{5}}=\ \ =3^{frac{3}{5}-(-frac{12}{5})}=3^{frac{3}{5}+frac{12}{5}}=3^{frac{15}{5}}=3^{3}=27[/latex] zad 4 [latex]a) 5sqrt{5}=5*5^{frac{1}{2}}=5^{1+frac{1}{2}}=5^{1frac{1}{2}}\ \ b) 49sqrt{7}=7^{2}*7^{frac{1}{2}}=7^{2+frac{1}{2}}=7^{2frac{1}{2}}\ \ c) 125sqrt[3]{5}=5^{3}*5^{frac{1}{3}}=5^{3+frac{1}{3}}=5^{3frac{1}{3}}\ \ d) 5sqrt[3]{25}=5*25^{frac{1}{3}}=5*(5^{2})^{frac{1}{3}}=5*5^{2*frac{1}{3}}=5*5^{frac{2}{3}}=5^{1+frac{2}{3}}=5^{1frac{2}{3}}\ [/latex] [latex]e) 16sqrt{8}=2^{4}*8^{frac{1}{2}}=2^{4}*(2^{3})^{frac{1}{2}}=2^{4}*2^{3*frac{1}{2}}=2^{4}*2^{frac{3}{2}}=2^{4+frac{3}{2}}=2^{5frac{1}{2}}[/latex] [latex] f) 8sqrt[3]{16}=2^{3}*(2^{4})^{frac{1}{3}}=2^{3}*2^{4*frac{1}{3}}=2^{3}*2^{frac{4}{3}}=2^{3+frac{4}{3}}=2^{4frac{1}{3}}\ \ g) frac{4}{sqrt[3]{2}}=2^{2}:2^{frac{1}{3}}=2^{2-frac{1}{3}}=2^{1frac{2}{3}}\ \ h) frac{sqrt[3]{2}}{2sqrt{2}}=2^{frac{1}{3}}:(2*2frac{1}{2})=2^{frac{1}{3}}:2^{1+frac{1}{2}}=2^{frac{1}{3}}:2^{frac{3}{2}}=2^{frac{1}{3}-frac{3}{2}}= 2^{frac{2}{6}-frac{9}{6}}=\ \ =2^{-frac{7}{6}}=2^{-1frac{1}{6}}[/latex]