Bonjour Ps4gaming25
Exercice 1
[tex]A=(3-4\times\dfrac{2}{3})\div\dfrac{1}{12}\\\\A=(3-\dfrac{8}{3})\times\dfrac{12}{1}\\\\A=(\dfrac{9}{3}-\dfrac{8}{3})\times12\\\\A=\dfrac{1}{3}\times12\\\\A=\dfrac{12}{3}\\\\\boxed{A=4}[/tex]
[tex]B=(4-\dfrac{2}{3})\times(2-\dfrac{4}{3})\\\\B=(\dfrac{12}{3}-\dfrac{2}{3})\times(\dfrac{6}{3}-\dfrac{4}{3})\\\\B=\dfrac{10}{3}\times\dfrac{2}{3}\\\\\boxed{B=\dfrac{20}{9}}[/tex]
[tex]C=\dfrac{13\times10^{14}\times10^6}{2\times(10^3)^7}\\\\C=\dfrac{13\times10^{14+6}}{2\times10^{3\times7}}\\\\C=\dfrac{13\times10^{20}}{2\times10^{21}}\\\\C=\dfrac{13}{2}\times\dfrac{10^{20}}{10^{21}}\\\\C=\dfrac{13}{2}\times10^{20-21}\\\\C=\dfrac{13}{2}\times10^{-1}\\\\C=\dfrac{13}{2}\times\dfrac{1}{10}\\\\\boxed{C=\dfrac{13}{20}=0,65}[/tex]
Exercice 2
[tex]1)\ D=\sqrt{1080}=\sqrt{36\times30}=\sqrt{36}\times\sqrt{30}=6\times\sqrt{30}\\\\\Longrightarrow\boxed{D=6\sqrt{30}}[/tex]
[tex]E=\sqrt{2}+3\sqrt{8}-6\sqrt{50}\\\\E=\sqrt{2}+3\sqrt{4\times2}-6\sqrt{25\times2}\\\\E=\sqrt{2}+3\sqrt{4}\times\sqrt{2}-6\sqrt{25}\times\sqrt{2}\\\\E=\sqrt{2}+3\times2\times\sqrt{2}-6\times5\times\sqrt{2}\\\\E=\sqrt{2}+6\sqrt{2}-30\sqrt{2}\\\\E=\boxed{-23\sqrt{2}}[/tex]
[tex]F=(2+\sqrt{3})^2\\\\F=2^2+2\times2\times\sqrt{3}+(\sqrt{3})^2\\\\F=4+4\sqrt{3}+3\\\\\boxed{F=7+4\sqrt{3}}[/tex]
[tex]G=(2+3\sqrt{3})(\sqrt{2}-1)\\\\G=2\times\sqrt{2}+2\times(-1)+3\sqrt{3}\times\sqrt{2}+3\sqrt{3}\times(-1)\\\\G=2\sqrt{2}-2+3\sqrt{3\times2}-3\sqrt{3}\\\\G=2\sqrt{2}-2+3\sqrt{6}-3\sqrt{3}\\\\\boxed{G=-2+2\sqrt{2}-3\sqrt{3}+3\sqrt{6}}[/tex]
[tex]2)\ H=\dfrac{10^5\times10^{-7}}{(10^3)^7}\\\\H=\dfrac{10^{5-7}}{10^{3\times7}}\\\\H=\dfrac{10^{-2}}{10^{21}}\\\\H=10^{-2-21}\\\\\boxed{H=10^{-23}}[/tex]
[tex]I=\dfrac{3^{2n+1}}{9^n}\\\\I=\dfrac{3^{2n+1}}{(3^2)^n}\\\\I=\dfrac{3^{2n+1}}{3^{2\times n}}\\\\I=\dfrac{3^{2n+1}}{3^{2n}}\\\\I=3^{2n+1-2n}\\\\\boxed{I=3^{1}=3}[/tex]
