1.
[tex]a) \ 6000000 = 6\cdot10^{76}\\\\b) \ 853200 = 8,532\cdot10^{5}\\\\c) \ 0,004 = 4\cdot10^{-3}\\\\d) \ 0,000360 = 3,6\cdot10^{-4}[/tex]
2.
[tex]a) \ \sqrt[3]{108}-\sqrt[3]{32} + \sqrt[3]{256} = \sqrt[3]{27\cdot4} -\sqrt[3]{9\cdot4}+\sqrt[3]{64\cdot4}=\sqrt[3]{3^{3}\cdot4}-\sqrt[3]{2^{3}\cdot4}+\sqrt[3]{4^{3}\cdot4}=\\\\=3\sqrt[3]{4}-2\sqrt[3]{4}+4\sqrt[3]{4} = 5\sqrt[3]{4}[/tex]
[tex]b) \ \frac{2^{13}\cdot16^{3}}{4^{10}} = \frac{2^{13}\cdot(2^{4})^{3}}{(2^{2})^{10}} = \frac{2^{13}\cdot2^{12}}{2^{20}} = \frac{2^{25}}{2^{20}} = 2^{5} = 32[/tex]
[tex]c) \ \sqrt{4\sqrt{4\sqrt{16}}}=\sqrt{4\sqrt{4\cdot4}} = \sqrt{4\cdot4}=4[/tex]
[tex]d) \ \frac{(6^{2})^{3}\cdot(6^{4})^{2}}{36^{3}\cdot6^{3}}=\frac{6^{6}\cdot6^{8}}{(6^{2})^{3}\cdot6^{3}}=\frac{6^{14}}{6^{6}\cdot6^{3}} = \frac{6^{14}}{6^{9}} = 6^{5} = 7776[/tex]
Wyjaśnienie:
[tex]a^{m}\cdot a^{m} = a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}\\\\(a^{m})^{n}=a^{m\cdot n}[/tex]
