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a)![243 ^{0.4}= (3 ^{5}) ^{ frac{2}{5} }= 3^{ frac{5*2}{5} }=3^{2}=9 243 ^{0.4}= (3 ^{5}) ^{ frac{2}{5} }= 3^{ frac{5*2}{5} }=3^{2}=9](https://tex.z-dn.net/?f=243+%5E%7B0.4%7D%3D+%283+%5E%7B5%7D%29+%5E%7B+frac%7B2%7D%7B5%7D+%7D%3D+3%5E%7B+frac%7B5%2A2%7D%7B5%7D+%7D%3D3%5E%7B2%7D%3D9++++)
Б)![( frac{64^{4} }{ 3^{8} } ) ^{- frac{1}{8} }= ( frac{( 8^{2}) ^{4} }{ 3^{8} } ) ^{- frac{1}{8} }=( frac{ 8^ ^{8} }{ 3^{8} } ) ^{- frac{1}{8} }=( (frac{8}{3} ) ^{8} ) ^{- frac{1}{8} } =(frac{8}{3} ) ^{- frac{8*1}{8} }=( frac{8}{3} )^{-1}= frac{3}{8} ( frac{64^{4} }{ 3^{8} } ) ^{- frac{1}{8} }= ( frac{( 8^{2}) ^{4} }{ 3^{8} } ) ^{- frac{1}{8} }=( frac{ 8^ ^{8} }{ 3^{8} } ) ^{- frac{1}{8} }=( (frac{8}{3} ) ^{8} ) ^{- frac{1}{8} } =(frac{8}{3} ) ^{- frac{8*1}{8} }=( frac{8}{3} )^{-1}= frac{3}{8}](https://tex.z-dn.net/?f=%28+frac%7B64%5E%7B4%7D+%7D%7B+3%5E%7B8%7D+%7D+%29+%5E%7B-+frac%7B1%7D%7B8%7D+%7D%3D+%28+frac%7B%28+8%5E%7B2%7D%29+%5E%7B4%7D+%7D%7B+3%5E%7B8%7D+%7D+%29+%5E%7B-+frac%7B1%7D%7B8%7D+%7D%3D%28+frac%7B+8%5E+%5E%7B8%7D+%7D%7B+3%5E%7B8%7D+%7D+%29+%5E%7B-+frac%7B1%7D%7B8%7D+%7D%3D%28+%28frac%7B8%7D%7B3%7D+%29+%5E%7B8%7D+%29+%5E%7B-+frac%7B1%7D%7B8%7D+%7D+%3D%28frac%7B8%7D%7B3%7D+%29+%5E%7B-+frac%7B8%2A1%7D%7B8%7D+%7D%3D%28+frac%7B8%7D%7B3%7D+%29%5E%7B-1%7D%3D+frac%7B3%7D%7B8%7D++)
в)![( 2^{4}) ^{ frac{5}{4} }=2 ^{5}=32 ( 2^{4}) ^{ frac{5}{4} }=2 ^{5}=32](https://tex.z-dn.net/?f=%28+2%5E%7B4%7D%29+%5E%7B+frac%7B5%7D%7B4%7D+%7D%3D2+%5E%7B5%7D%3D32++)
г)![( frac{27^{3} }{125^ {6} })^{ frac{2}{9} }= ( frac{3 ^{9} }{5 ^{18} })^{ frac{2}{9} }=( frac{3}{ 5^{2} }) ^{ frac{9*2}{9} }=( frac{3}{25}) ^{2} = frac{9}{625} ( frac{27^{3} }{125^ {6} })^{ frac{2}{9} }= ( frac{3 ^{9} }{5 ^{18} })^{ frac{2}{9} }=( frac{3}{ 5^{2} }) ^{ frac{9*2}{9} }=( frac{3}{25}) ^{2} = frac{9}{625}](https://tex.z-dn.net/?f=%28+frac%7B27%5E%7B3%7D+%7D%7B125%5E+%7B6%7D+%7D%29%5E%7B+frac%7B2%7D%7B9%7D+%7D%3D++%28+frac%7B3+%5E%7B9%7D+%7D%7B5+%5E%7B18%7D+%7D%29%5E%7B+frac%7B2%7D%7B9%7D+%7D%3D%28+frac%7B3%7D%7B+5%5E%7B2%7D+%7D%29+%5E%7B+frac%7B9%2A2%7D%7B9%7D+%7D%3D%28+frac%7B3%7D%7B25%7D%29+%5E%7B2%7D+++%3D+frac%7B9%7D%7B625%7D++++)
д)![8 ^{ frac{1}{2} }*8^{- frac{1}{6} }*9 ^{- frac{3}{2} }= 8 ^{ frac{1}{2} + frac{1}{6} } *3 ^{- frac{3*2}{2} } =(2 ^{3}) ^{ frac{4}{6} }*3 ^{-3} =2 ^{ frac{2*3}{3} }* frac{1}{27}= frac{4}{27} 8 ^{ frac{1}{2} }*8^{- frac{1}{6} }*9 ^{- frac{3}{2} }= 8 ^{ frac{1}{2} + frac{1}{6} } *3 ^{- frac{3*2}{2} } =(2 ^{3}) ^{ frac{4}{6} }*3 ^{-3} =2 ^{ frac{2*3}{3} }* frac{1}{27}= frac{4}{27}](https://tex.z-dn.net/?f=8+%5E%7B+frac%7B1%7D%7B2%7D+%7D%2A8%5E%7B-+frac%7B1%7D%7B6%7D+%7D%2A9+%5E%7B-+frac%7B3%7D%7B2%7D+%7D%3D+++8+%5E%7B+frac%7B1%7D%7B2%7D+%2B+frac%7B1%7D%7B6%7D+%7D+%2A3+%5E%7B-+frac%7B3%2A2%7D%7B2%7D+%7D+%3D%282+%5E%7B3%7D%29+%5E%7B+frac%7B4%7D%7B6%7D+%7D%2A3+%5E%7B-3%7D+++%3D2+%5E%7B+frac%7B2%2A3%7D%7B3%7D+%7D%2A+frac%7B1%7D%7B27%7D%3D+frac%7B4%7D%7B27%7D+++)
е)![(2*5) ^{ frac{2}{3} }* 2^{ frac{8}{3*2} } *5 ^{- frac{5}{3} }= 2^{ frac{2}{3} }*5 ^{ frac{2}{3} }* 2^{ frac{4}{3} } *5 ^{- frac{5}{3} }=2^{ frac{2+4}{3} }*5 ^{ frac{2-5}{3} }=2^{ frac{6}{3} }*5 ^{ frac{-}{3} }= (2*5) ^{ frac{2}{3} }* 2^{ frac{8}{3*2} } *5 ^{- frac{5}{3} }= 2^{ frac{2}{3} }*5 ^{ frac{2}{3} }* 2^{ frac{4}{3} } *5 ^{- frac{5}{3} }=2^{ frac{2+4}{3} }*5 ^{ frac{2-5}{3} }=2^{ frac{6}{3} }*5 ^{ frac{-}{3} }=](https://tex.z-dn.net/?f=%282%2A5%29+%5E%7B+frac%7B2%7D%7B3%7D+%7D%2A+2%5E%7B+frac%7B8%7D%7B3%2A2%7D+%7D++%2A5+%5E%7B-+frac%7B5%7D%7B3%7D+%7D%3D+2%5E%7B+frac%7B2%7D%7B3%7D+%7D%2A5+%5E%7B+frac%7B2%7D%7B3%7D+%7D%2A+2%5E%7B+frac%7B4%7D%7B3%7D+%7D++%2A5+%5E%7B-+frac%7B5%7D%7B3%7D+%7D%3D2%5E%7B+frac%7B2%2B4%7D%7B3%7D+%7D%2A5+%5E%7B+frac%7B2-5%7D%7B3%7D+%7D%3D2%5E%7B+frac%7B6%7D%7B3%7D+%7D%2A5+%5E%7B+frac%7B-%7D%7B3%7D+%7D%3D)
![2 ^{2}*5 ^{-1} = frac{4}{5} 2 ^{2}*5 ^{-1} = frac{4}{5}](https://tex.z-dn.net/?f=2+%5E%7B2%7D%2A5+%5E%7B-1%7D++%3D+frac%7B4%7D%7B5%7D+)
Ж)![8 ^{ frac{7}{3} }: (3^{4}) ^{ frac{3}{4} }=2 ^{ frac{3*7}{3} }: 3^{3} = frac{2 ^{7} }{27} = frac{128}{27} 8 ^{ frac{7}{3} }: (3^{4}) ^{ frac{3}{4} }=2 ^{ frac{3*7}{3} }: 3^{3} = frac{2 ^{7} }{27} = frac{128}{27}](https://tex.z-dn.net/?f=8+%5E%7B+frac%7B7%7D%7B3%7D+%7D%3A+%283%5E%7B4%7D%29+%5E%7B+frac%7B3%7D%7B4%7D+%7D%3D2+%5E%7B+frac%7B3%2A7%7D%7B3%7D+%7D%3A+3%5E%7B3%7D+%3D++frac%7B2+%5E%7B7%7D+%7D%7B27%7D+%3D+frac%7B128%7D%7B27%7D+)
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