Proszę o rozwiązanie. Od razu daje NAJ!!!

[tex]5^{\frac{1}{3} }\cdot\sqrt[4]{5^{2}}:\sqrt{5} \cdot\sqrt[3]{5^{2}}= 5^{\frac{1}{3} }\cdot5^{\frac{2}{4} }:5^{\frac{1}{2} }\cdot5^{\frac{2}{3} }=5^{\frac{1}{3}+\frac{1}{2}-\frac{1}{2}+\frac{2}{3} }=5^{\frac{1}{3}+\frac{2}{3} }=5^{1}=5[/tex]

[tex](\sqrt[3]{27}\cdot\sqrt{27^{3}} ):(27^{\frac{1}{2} } \cdot\sqrt[4]{27^{2}} \cdot\sqrt{27})=(27^{\frac{1}{3} }\cdot27^{\frac{3}{2} }):(27^{\frac{1}{2} }\cdot27^{\frac{2}{4} } \cdot27^{\frac{1}{2} })=\\\\=27^{\frac{2}{6}+\frac{9}{6} }:27^{\frac{1}{2}+\frac{1}{2}+\frac{1}{2} }=27^{\frac{11}{6} }:27^{\frac{3}{2} }=27^{\frac{11}{6}-\frac{9}{6} }=27^{\frac{2}{6} }=27^{\frac{1}{3} }=(3^{3})^{\frac{1}{3} }=\\\\=3^{3\cdot\frac{1}{3} }=3^{\frac{3}{3} }=3^{1}=3[/tex]

[tex](\sqrt{7} :\sqrt[3]{7^{2}}\cdot49\cdot7^{6}):(49^{3} \cdot7^{\frac{5}{6} })=(7^{\frac{1}{2} }:7^{\frac{2}{3} }\cdot7^{2}\cdot7^{6}):((7^{2})^{3}\cdot7^{\frac{5}{6} })=\\\\=(7^\frac{3}{6}:7^{\frac{4}{6} }\cdot7^{2}\cdot7^{6}):(7^{2\cdot3}\cdot7^{\frac{5}{6} })=7^{\frac{3}{6}-\frac{4}{6}+2+6 }:7^{6+\frac{5}{6} }=7^{7\frac{5}{6} }:7^{6\frac{5}{6} }=\\\\=7^{7\frac{5}{6}-6\frac{5}{6} }=7^{1}=7[/tex]

[tex]\cfrac{3^{1\frac{1}{2} }\cdot3^{\frac{1}{3} }\cdot\sqrt{3} }{\sqrt[3]{3^{2}}:\sqrt[3]{3} } =\cfrac{3^{\frac{3}{2} }\cdot3^{\frac{1}{3} }\cdot3^{\frac{1}{2} } }{3^{\frac{2}{3} }:3^{\frac{1}{3} } } =\cfrac{3^{\frac{3}{2} +\frac{1}{3} +\frac{1}{2} } }{3^{\frac{2}{3} -\frac{1}{3} } } =\cfrac{3^{2\frac{1}{3} } }{3^{\frac{1}{3} } } =3^{2\frac{1}{3}-\frac{1}{3} }=3^{2}=9[/tex]

Wykorzystane własności:

[tex]a^{x}\cdot a^{y}=a^{x+y}[/tex]

[tex]a^{x}:a^{y}=a^{x-y}[/tex]

[tex](a^{x})^{y}=a^{x\cdot y}[/tex]

[tex]\sqrt[y]{a^{x}}=a^{\frac{x}{y} }[/tex]