Вычислите: [latex]\frac{5^{8,5}}{125^{3,5}}[/latex] [latex]\frac{m^{\frac{2}{5}}*m^{\frac{3}{7}}}{m^{\frac{8}{35}}}[/latex] при m=32 [latex]\frac{27^{2,3}}{3^{3,9}}[/latex] [latex]\frac{m^{\frac{2}{3}}*m^{\frac{13}{14}}}{m^{\fr...

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[latex]\frac{5^{8,5}}{125^{3,5}}=\frac{5^{8,5}}{(5^3)^{3,5}}=\frac{5^{8,5}}{5^{10,5}}=\frac{1}{5^2}=\frac{1}{25} [/latex]   [latex]\frac{m^{\frac{2}{5}}*m^{\frac{3}{7}}}{m^{\frac{8}{35}}}=m^{\frac{2}{5}+\frac{3}{7}-\frac{8}{35}}=m^{\frac{14}{35}+\frac{15}{35}-\frac{8}{35}}=m^{\frac{21}{35}}=m^{\frac{3}{5}}\\\ \\\ m=32\\\ \\\ 32^{\frac{3}{5}}=(2^5)^{\frac{3}{5}}=2^3=8[/latex]   [latex]\frac{27^{2,3}}{3^{3,9}}=\frac{(3^3)^{2,3}}{3^{3,9}}=\frac{3^{6,9}}{3^{3,9}}=3^3=27[/latex]   [latex]\frac{m^{\frac{2}{3}}*m^{\frac{13}{14}}}{m^{\frac{2}{21}}}=m^{\frac{2}{3}+\frac{13}{14}-\frac{2}{21}}=m^{\frac{28}{42}+\frac{39}{42}-\frac{4}{42}}=m^{\frac{63}{42}}=m^{\frac{3}{2}}\\\ m=49\\\ 49^{\frac{3}{2}}=(7^2)^{\frac{3}{2}}=7^3=343[/latex]