[tex](125^3*5^{-4}):(25^2*0,2^{-3})=((5^3)^3*5^{-4}):((5^2)^2*(\frac{1}{5})^{-3})=\\\\=(5^{3*3}*5^{-4}):(5^{2*2}*5^3)=(5^9*5^{-4}):(5^4*5^3)=5^{9-4}:5^{4+3}=5^5:5^7=\\\\=5^{5-7}=5^{-2}=(\frac{1}{5})^2=\frac{1}{25}[/tex]
[tex]\frac{1,75+0,5*(\frac{2}{3})^{-1}}{3\frac{1}{12}-3*(\frac{2}{3})^2}=\frac{1,75+0,5*\frac{3}{2}}{3\frac{1}{12}-3*\frac{4}{9}}=\frac{1\frac{3}{4}+\frac{1}{2}*\frac{3}{2}}{3\frac{1}{12}-\frac{4}{3}}=\frac{1\frac{3}{4}+\frac{3}{4}}{\frac{37}{12}-\frac{16}{12}}=\frac{1\frac{6}{4}}{\frac{21}{12}}=\frac{1\frac{3}{2}}{\frac{7}{4}}=\frac{5}{2}*\frac{4}{7}=\\\\=\frac{5}{1}*\frac{2}{7}=\frac{10}{7}=1\frac{3}{7}[/tex]
[tex]\sqrt{48}*\sqrt{12}=\sqrt{48*12}=\sqrt{576}=24[/tex]
[tex](3\sqrt2-8)(3\sqrt2+8)=(3\sqrt2)^2-8^2=9*2-64=18-64=-46[/tex]
[tex](x+\sqrt3)^2+2x(x+3)(x-3)=x^2+2*x*\sqrt3+(\sqrt3)^2+2x(x^2-3^2)=\\\\=x^2+2\sqrt3x+3+2x(x^2-9)=x^2+2\sqrt3x+3+2x^3-18x=\\\\=2x^3+x^2+(2\sqrt3-18)x+3[/tex]
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[tex](125^3*5^{-4}):(25^2*0,2^{-3})=((5^3)^3*5^{-4}):((5^2)^2*(\frac{1}{5})^{-3})=\\\\=(5^{3*3}*5^{-4}):(5^{2*2}*5^3)=(5^9*5^{-4}):(5^4*5^3)=5^{9-4}:5^{4+3}=5^5:5^7=\\\\=5^{5-7}=5^{-2}=(\frac{1}{5})^2=\frac{1}{25}[/tex]
[tex]\frac{1,75+0,5*(\frac{2}{3})^{-1}}{3\frac{1}{12}-3*(\frac{2}{3})^2}=\frac{1,75+0,5*\frac{3}{2}}{3\frac{1}{12}-3*\frac{4}{9}}=\frac{1\frac{3}{4}+\frac{1}{2}*\frac{3}{2}}{3\frac{1}{12}-\frac{4}{3}}=\frac{1\frac{3}{4}+\frac{3}{4}}{\frac{37}{12}-\frac{16}{12}}=\frac{1\frac{6}{4}}{\frac{21}{12}}=\frac{1\frac{3}{2}}{\frac{7}{4}}=\frac{5}{2}*\frac{4}{7}=\\\\=\frac{5}{1}*\frac{2}{7}=\frac{10}{7}=1\frac{3}{7}[/tex]
[tex]\sqrt{48}*\sqrt{12}=\sqrt{48*12}=\sqrt{576}=24[/tex]
[tex](3\sqrt2-8)(3\sqrt2+8)=(3\sqrt2)^2-8^2=9*2-64=18-64=-46[/tex]
[tex](x+\sqrt3)^2+2x(x+3)(x-3)=x^2+2*x*\sqrt3+(\sqrt3)^2+2x(x^2-3^2)=\\\\=x^2+2\sqrt3x+3+2x(x^2-9)=x^2+2\sqrt3x+3+2x^3-18x=\\\\=2x^3+x^2+(2\sqrt3-18)x+3[/tex]