[tex]Bonjour;\\\\\\a)\\\\\\2,5\times10^{-4}\times(4\times10)^2=2,5\times10^{-4}\times4\times4\times10^2\\\\\\=2,5\times4\times4\times10^{-4+2}=10\times4\times10^{-2}=4\times10^{1-2}\\\\\\=4\times10^{-1}=0,4\ .[/tex]
[tex]b)\\\\\\3+\dfrac{1}{6+\dfrac{1}{15}}=3+\dfrac{1}{\dfrac{90}{15}+\dfrac{1}{15}}=3+\dfrac{1}{\dfrac{91}{15}}=\dfrac{273}{91}+\dfrac{15}{91}=\dfrac{288}{91}\ .[/tex]
c)
[tex]\sqrt{\dfrac{121}{49}}\times(\sqrt{72}\times\dfrac{1}{\sqrt2})=\sqrt{\dfrac{11^2}{7^2}}\times\sqrt{\dfrac{72}{2}}=\dfrac{11}{7}\times\sqrt{36}\\\\\\=\dfrac{11}{7}\times\sqrt{6^2}=\dfrac{11}{7}\times6=\dfrac{66}{7}\ .[/tex]
[tex]d)\\\\\\\dfrac{3^{10}\times(3^{-7})^2}{(3^2)^{-4}}=\dfrac{3^{10}\times3^{-14}}{3^{-8}}=3^{10-14+8}=3^4\ .[/tex]
[tex]2)\\\\\\(3\sqrt2-5)^2=(3\sqrt2)^2-2\times3\sqrt2\times5+5^2\\\\\\=18-30\sqrt2+25=43-30\sqrt2\ .[/tex]
