[tex]a) \ (1,4)^{7}:(1,4)^{5} = (1,4)^{7-5} = (1,4)^{2} = 1,4\cdot1,4 = 1,96\\\\\\b) \ (\frac{2}{7})^{5}\cdot7^{5} = (\frac{2}{7}\cdot7)^{5} = 2^{5} = 32[/tex]
[tex]c) \ (\frac{2}{7})^{5}\cdot(3\frac{1}{2})^{6} = (\frac{7}{2})^{-5}\cdot(\frac{7}{2})^{6} = (\frac{7}{2})^{-5+6}=(\frac{7}{2})^{1} = \frac{7}{2} = 3\frac{1}{2}\\\\\\d) \ \frac{36^{2}\cdot6^{4}}{6^{5}} =\frac{ (6^{2})^{2}\cdot6^{4}}{6^{5}} =\frac{6^{4}\cdot6^{4}}{6^{5}} = \frac{6^{8}}{6^{5}} = 6^{3} = 216[/tex]
Wykorzystane wzory:
[tex]a^{n}:b^{n} = (a:b)^{n}\\\\a^{n}\cdot b^{n} = (a\cdot b)^{n}\\\\(\frac{a}{b})^{n} = (\frac{b}{a})^{-n}[/tex]
[tex]a^{m}\cdot a^{m} = a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}\\\\(a^{m})^{n} = a^{m\cdot n}[/tex]
