[tex]a)\\\\\frac{18^{4}\cdot49^{2}}{6^{4}}:7^{4} =\frac{18^{4}\cdot(7^{2})^{2}}{6^{4}}:7^{4} = \frac{18^{4}\cdot7^{4}}{6^{4}}\cdot\frac{1}{7^{4}} = \frac{18^{4}}{6^{4}} = (\frac{18}{6})^{4}} = 3^{4} = 81\\\\\\b)\\\\\sqrt[3]{\frac{2}{3}}:\sqrt[3]{\frac{9}{4}} = \sqrt[3]{\frac{2}{3}:\frac{9}{4}} = \sqrt[3]{\frac{2}{3}\cdot\frac{4}{9}} = \sqrt[3]{\frac{8}{27}} = \sqrt[3]{(\frac{2}{3})^{3}} = \frac{2}{3}\\\\\\c)\\\\2^{\frac{3}{2}}\cdot\sqrt{2} = 2^{\frac{3}{2}}\cdot2^{\frac{1}{2}}=2^{\frac{4}{2}} = 2^{2} = 4[/tex]
Wyjaśnienie:
[tex]a^{m}\cdot a^{n} = a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}\\\\(a^{m})^{n} = a^{m\cdot n[/tex]
