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1a) ![sqrt[5]{ x^{3} } * sqrt{x} = x ^{ frac{3}{5} }*x ^{ frac{1}{2} }= x ^{ frac{6}{10}+ frac{5}{10} }= x ^{ frac{11}{10} }= sqrt[10]{ x^{11} } =x sqrt[10]{x} sqrt[5]{ x^{3} } * sqrt{x} = x ^{ frac{3}{5} }*x ^{ frac{1}{2} }= x ^{ frac{6}{10}+ frac{5}{10} }= x ^{ frac{11}{10} }= sqrt[10]{ x^{11} } =x sqrt[10]{x}](https://tex.z-dn.net/?f=+sqrt%5B5%5D%7B+x%5E%7B3%7D+%7D+%2A+sqrt%7Bx%7D+%3D+x+%5E%7B+frac%7B3%7D%7B5%7D+%7D%2Ax+%5E%7B+frac%7B1%7D%7B2%7D+%7D%3D+x+%5E%7B+frac%7B6%7D%7B10%7D%2B+frac%7B5%7D%7B10%7D++%7D%3D+x+%5E%7B+frac%7B11%7D%7B10%7D+%7D%3D+sqrt%5B10%5D%7B+x%5E%7B11%7D+%7D+%3Dx+sqrt%5B10%5D%7Bx%7D+++++)
б)![frac{ x^{0,5} }{( sqrt[4]{x}) ^{2} } = frac{ sqrt{x} }{ sqrt{x} } = 1 frac{ x^{0,5} }{( sqrt[4]{x}) ^{2} } = frac{ sqrt{x} }{ sqrt{x} } = 1](https://tex.z-dn.net/?f=+frac%7B+x%5E%7B0%2C5%7D+%7D%7B%28+sqrt%5B4%5D%7Bx%7D%29+%5E%7B2%7D+%7D+%3D++frac%7B+sqrt%7Bx%7D+%7D%7B+sqrt%7Bx%7D+%7D+%3D+1)
2a)![frac{3 ^{ frac{2}{3} }*81 ^{ frac{3}{4} } }{3 ^{- frac{1}{3} } }= frac{3 ^{ frac{2}{3} }*(3 ^{4}) ^{ frac{3}{4} } }{3 ^{- frac{1}{3} } }=3 ^{ frac{2}{3}+ frac{1}{3} }*3 ^{3}=3*3 ^{3}=81 frac{3 ^{ frac{2}{3} }*81 ^{ frac{3}{4} } }{3 ^{- frac{1}{3} } }= frac{3 ^{ frac{2}{3} }*(3 ^{4}) ^{ frac{3}{4} } }{3 ^{- frac{1}{3} } }=3 ^{ frac{2}{3}+ frac{1}{3} }*3 ^{3}=3*3 ^{3}=81](https://tex.z-dn.net/?f=+frac%7B3+%5E%7B+frac%7B2%7D%7B3%7D+%7D%2A81+%5E%7B+frac%7B3%7D%7B4%7D+%7D++%7D%7B3+%5E%7B-+frac%7B1%7D%7B3%7D+%7D+%7D%3D+frac%7B3+%5E%7B+frac%7B2%7D%7B3%7D+%7D%2A%283+%5E%7B4%7D%29+%5E%7B+frac%7B3%7D%7B4%7D+%7D+++%7D%7B3+%5E%7B-+frac%7B1%7D%7B3%7D+%7D+%7D%3D3+%5E%7B+frac%7B2%7D%7B3%7D%2B+frac%7B1%7D%7B3%7D++%7D%2A3+%5E%7B3%7D%3D3%2A3+%5E%7B3%7D%3D81+++++)
б)![(10 ^{- frac{1}{3} } *0,01 ^{ frac{1}{3} }) ^{-1} =[10 ^{- frac{1}{3} }*(10 ^{-2}) ^{ frac{1}{3} }] ^{-1} =(10 ^{- frac{1}{3} } *10 ^{- frac{2}{3} } ) ^{-1} =(10 ^{-1}) ^{-1} (10 ^{- frac{1}{3} } *0,01 ^{ frac{1}{3} }) ^{-1} =[10 ^{- frac{1}{3} }*(10 ^{-2}) ^{ frac{1}{3} }] ^{-1} =(10 ^{- frac{1}{3} } *10 ^{- frac{2}{3} } ) ^{-1} =(10 ^{-1}) ^{-1}](https://tex.z-dn.net/?f=%2810+%5E%7B-+frac%7B1%7D%7B3%7D+%7D+%2A0%2C01+%5E%7B+frac%7B1%7D%7B3%7D+%7D%29+%5E%7B-1%7D+%3D%5B10+%5E%7B-+frac%7B1%7D%7B3%7D+%7D%2A%2810+%5E%7B-2%7D%29+%5E%7B+frac%7B1%7D%7B3%7D+%7D%5D+%5E%7B-1%7D+%3D%2810+%5E%7B-+frac%7B1%7D%7B3%7D+%7D+%2A10+%5E%7B-+frac%7B2%7D%7B3%7D+%7D+%29+%5E%7B-1%7D+%3D%2810+%5E%7B-1%7D%29+%5E%7B-1%7D++++++)
![10 10](https://tex.z-dn.net/?f=10)
3)![(16x) ^{ frac{3}{4} }*( frac{1}{8} x ^{ frac{3}{8} } ) ^{- frac{2}{3} }=(2 ^{4}) ^{ frac{3}{4} } *x ^{ frac{3}{4} }*(2 ^{-3}) ^{- frac{2}{3} }*(x ^{ frac{3}{8} }) ^{- frac{2}{3} } = 2 ^{3}*x ^{ frac{3}{4} } *2 ^{2}*x ^{- frac{1}{4} } (16x) ^{ frac{3}{4} }*( frac{1}{8} x ^{ frac{3}{8} } ) ^{- frac{2}{3} }=(2 ^{4}) ^{ frac{3}{4} } *x ^{ frac{3}{4} }*(2 ^{-3}) ^{- frac{2}{3} }*(x ^{ frac{3}{8} }) ^{- frac{2}{3} } = 2 ^{3}*x ^{ frac{3}{4} } *2 ^{2}*x ^{- frac{1}{4} }](https://tex.z-dn.net/?f=%2816x%29+%5E%7B+frac%7B3%7D%7B4%7D+%7D%2A%28+frac%7B1%7D%7B8%7D+x+%5E%7B+frac%7B3%7D%7B8%7D+%7D+%29+%5E%7B-+frac%7B2%7D%7B3%7D+%7D%3D%282+%5E%7B4%7D%29+%5E%7B+frac%7B3%7D%7B4%7D+%7D+%2Ax+%5E%7B+frac%7B3%7D%7B4%7D+%7D%2A%282+%5E%7B-3%7D%29+%5E%7B-+frac%7B2%7D%7B3%7D+%7D%2A%28x+%5E%7B+frac%7B3%7D%7B8%7D+%7D%29+%5E%7B-+frac%7B2%7D%7B3%7D+%7D+%3D+2+%5E%7B3%7D%2Ax+%5E%7B+frac%7B3%7D%7B4%7D+%7D+%2A2+%5E%7B2%7D%2Ax+%5E%7B-+frac%7B1%7D%7B4%7D+%7D+++++++++)
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