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![sqrt{x^{3}} * sqrt{x} = x^{ frac{3}{2} } *x^{ frac{1}{2} }=x^{ frac{3}{2}+frac{1}{2} }=x^{2}. \
frac{x^{0.5}}{( sqrt[4]{x})^{2} } = frac{x^{ frac{1}{2}}}{(x^{ frac{1}{4} })^{2} } = frac{x^{ frac{1}{2}}}{x^{ frac{1}{4}*2 }}=frac{x^{ frac{1}{2}}}{x^{ frac{1}{2}}}=x^{ frac{1}{2}-frac{1}{2} }=x^{0}. sqrt{x^{3}} * sqrt{x} = x^{ frac{3}{2} } *x^{ frac{1}{2} }=x^{ frac{3}{2}+frac{1}{2} }=x^{2}. \
frac{x^{0.5}}{( sqrt[4]{x})^{2} } = frac{x^{ frac{1}{2}}}{(x^{ frac{1}{4} })^{2} } = frac{x^{ frac{1}{2}}}{x^{ frac{1}{4}*2 }}=frac{x^{ frac{1}{2}}}{x^{ frac{1}{2}}}=x^{ frac{1}{2}-frac{1}{2} }=x^{0}.](https://tex.z-dn.net/?f=+sqrt%7Bx%5E%7B3%7D%7D+%2A+sqrt%7Bx%7D+%3D+x%5E%7B+frac%7B3%7D%7B2%7D+%7D+%2Ax%5E%7B+frac%7B1%7D%7B2%7D+%7D%3Dx%5E%7B+frac%7B3%7D%7B2%7D%2Bfrac%7B1%7D%7B2%7D+%7D%3Dx%5E%7B2%7D.+%5C+%0A+frac%7Bx%5E%7B0.5%7D%7D%7B%28+sqrt%5B4%5D%7Bx%7D%29%5E%7B2%7D+%7D+%3D+frac%7Bx%5E%7B+frac%7B1%7D%7B2%7D%7D%7D%7B%28x%5E%7B+frac%7B1%7D%7B4%7D+%7D%29%5E%7B2%7D+%7D+%3D+frac%7Bx%5E%7B+frac%7B1%7D%7B2%7D%7D%7D%7Bx%5E%7B+frac%7B1%7D%7B4%7D%2A2+%7D%7D%3Dfrac%7Bx%5E%7B+frac%7B1%7D%7B2%7D%7D%7D%7Bx%5E%7B+frac%7B1%7D%7B2%7D%7D%7D%3Dx%5E%7B+frac%7B1%7D%7B2%7D-frac%7B1%7D%7B2%7D+%7D%3Dx%5E%7B0%7D.)
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![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}}}=frac{3^{frac{2}{3}}*3^{4*frac{3}{4}}}{3^{-frac{1}{3}}}==frac{3^{frac{2}{3}}*3^{3}}{3^{-frac{1}{3}}}=3^{frac{2}{3}+3-(-frac{1}{3})}=3^{4}=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}}}=frac{3^{frac{2}{3}}*3^{4*frac{3}{4}}}{3^{-frac{1}{3}}}==frac{3^{frac{2}{3}}*3^{3}}{3^{-frac{1}{3}}}=3^{frac{2}{3}+3-(-frac{1}{3})}=3^{4}=81.](https://tex.z-dn.net/?f=frac%7B3%5E%7Bfrac%7B2%7D%7B3%7D%7D%2A81%5E%7Bfrac%7B3%7D%7B4%7D%7D%7D%7B3%5E%7B-frac%7B1%7D%7B3%7D%7D%7D%3Dfrac%7B3%5E%7Bfrac%7B2%7D%7B3%7D%7D%2A%283%5E%7B4%7D%29%5E%7Bfrac%7B3%7D%7B4%7D%7D%7D%7B3%5E%7B-frac%7B1%7D%7B3%7D%7D%7D%3Dfrac%7B3%5E%7Bfrac%7B2%7D%7B3%7D%7D%2A3%5E%7B4%2Afrac%7B3%7D%7B4%7D%7D%7D%7B3%5E%7B-frac%7B1%7D%7B3%7D%7D%7D%3D%3Dfrac%7B3%5E%7Bfrac%7B2%7D%7B3%7D%7D%2A3%5E%7B3%7D%7D%7B3%5E%7B-frac%7B1%7D%7B3%7D%7D%7D%3D3%5E%7Bfrac%7B2%7D%7B3%7D%2B3-%28-frac%7B1%7D%7B3%7D%29%7D%3D3%5E%7B4%7D%3D81.)
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