1.
[tex]0,03^{2} = 0,03\times0,03 = 0,0009\\\\3^{-5} = (\frac{1}{3})^{5} = \frac{1^{5}}{3^{5}} = \frac{1}{243}\\\\(2\frac{1}{2})^{3} = (\frac{5}{2})^{3} = \frac{125}{8} = 15\frac{5}{8}}\\\\(\frac{2}{5})^{-3} = (\frac{5}{2})^{3} = \frac{125}{8} = 15\frac{5}{8}[/tex]
2.
[tex]27\cdot3^{6} = 3^{3}\cdot3^{6} = 3^{3+6} = 3^{9}\\\\64:2^{3} = 2^{6}:2^{3} = 2^{6-3} = 2^{3}\\\\15^{3}\cdot(\frac{1}{5})^{5} = 15^{3}\cdot(\frac{1}{5})^{3}\cdot(\frac{1}{5})^{2}=(15\cdot\frac{1}{5})^{3}\cdot(\frac{1}{5})^{2} = 1^{3}\cdot(\frac{1}{5})^{2} = 1\cdot(\frac{1}{5})^{2}=(\frac{1}{5})^{2}[/tex]
3.
[tex]25^{3} = (5^{2})^{3} = 5^{2\cdot3} = 5^{6}\\\\10000^{7} = (10^{4})^{7} = 10^{4\cdot7} = 10^{28}\\\\(5^{7}\cdot25)^{2} =(5^{7}\cdot5^{2})^{2} = (5^{7+2})^{2} = (5^{9})^{2} = 5^{9\cdot2} = 5^{18}\\\\(\frac{5^{8}}{125})^{4} = (\frac{5^{8}}{5^{3}})^{4} = (5^{5})^{4} = 5^{20}[/tex]
4.
[tex]a) \ 578000000 = 5,78\cdot10^{8}\\\\b) \ 0,000000723 = 7,23\cdot10^{-7}[/tex]
