18.
[tex]8^{-5}\cdot4^{7} =(2^{3})^{-5} \cdot(2^{2})^{7} = 2^{-15}\cdot2^{14} = 2^{-15+14} = 2^{-1} = \boxed{\frac{1}{2}}\\\\\underline{Odp. \ B.}[/tex]
19.
[tex]\frac{7^{6}\cdot6^{7}}{42^{6}} = \frac{7^{6}\cdot6^{6}}{42^{6}}\cdot6 = \frac{(7\cdot6)^{6}}{42^{6}}\cdot6 = \frac{42^{6}}{42^{6}}\cdot6 = \boxed{6}\\\\\underline{Odp. \ C.}[/tex]
20.
[tex]\sqrt[3]{\frac{7}{3}}\cdot\sqrt[3]{\frac{81}{56}} = \sqrt[3]{\frac{7}{3}\cdot\frac{81}{56}} = \sqrt[3]{\frac{7}{56}\cdot\frac{81}{3}} = \sqrt[3]{\frac{1}{8}\cdot27} = \sqrt[3]{\frac{27}{8}} = \sqrt[3]{\frac{3^{3}}{2^{3}}} = \frac{3}{2} = \boxed{1,5}\\\\\underline{Odp. \ C.}[/tex]
Wyjaśnienie
Wykorzystano własności potęg:
[tex]a^{n}\cdot a^{m} = a^{n+m}\\\\a^{n}\cdot b^{n} = (a\cdot b)^{n}\\\\(a^{n})^{m} = a^{n\cdot m}\\\\\sqrt[n]{a}\cdot\sqrt[n]{b} = \sqrt[n]{a\cdot b}}[/tex]
