1.
[tex]a) \ (-\frac{2}{3})^{3} = (-\frac{2}{3})\cdot(-\frac{2}{3})\cdot(-\frac{2}{3}) = -\frac{8}{27}\\\\b) \ (-0,1)^{3} = -0,001[/tex]
2.
[tex]a) \ 2^{3}\cdot2\cdot2 =2^{3+1+1} =2^{5}\\\\b) \ (3^{4})^{2} = 3^{4\cdot2} = 3^{8}\\\\c) \ 5^{7}:5^{3} = 5^{7-3} = 5^{4}\\\\d) \ 4^{3}\cdot4^{5}:4^{2} = 4^{3+5-2} =4^{6}[/tex]
3.
[tex]a) \ 6 \ 100 \ 000 \ 000 = 6,1\cdot10^{9}\\\\b) \ 12 \ 000 \ 000 = 1,2\cdot10^{7}[/tex]
4.
[tex]a) \ \sqrt{4}+\sqrt{36} = 2+6 = 8\\\\b) \ \sqrt{2500} = 50\\\\c) \ \sqrt{4\cdot5\cdot5\cdot4}} =\sqrt{4^{2}\cdot5^{2}} = 4\cdot5 = 20\\\\d) \ \sqrt{9}\cdot\sqrt{16} =3\cdot4 = 12\\\\e) \ \sqrt{7} + 3\sqrt{7} = 4\sqrt{7}\\\\f) \ 9\sqrt{2}-4\sqrt{2}-2\sqrt{2} = 9\sqrt{2}-6\sqrt{2} = 3\sqrt{2}[/tex]
5.
[tex]a) \ \sqrt{32} = \sqrt{16\cdot2} = \sqrt{16}\cdot\sqrt{2} = 4\sqrt{2}\\\\b) \ \sqrt[3]{56} = \sqrt[3]{8\cdot7} = \sqrt[3]{8}\cdot\sqrt[3]{7} = 2\sqrt[3]{7}[/tex]
6.
[tex]a) \ 2\sqrt{5} = \sqrt{2^{2}\cdot5} = \sqrt{4\cdot5} = \sqrt{20}\\\\b) \ 2\sqrt[3]{5}=\sqrt[3]{2^{3}\cdot5} = \sqrt[3]{8\cdot5} = \sqrt[3]{40}[/tex]
