Cho a, b là những số thực dương. Rút gọn các biểu thức sau:
\(a)\ \dfrac{a^{\dfrac{4}{3}}(a^{\dfrac{-1}{3}}+a^{\dfrac{2}{3}})}{a^{\dfrac{1}{4}}(a^{\dfrac{3}{4}}+a^{\dfrac{-1}{4}})}\)
\(b)\ \dfrac{b^{\dfrac{1}{5}} (\sqrt[5]{b^4}-\sqrt[5]{b^{-1}})}{b^{\dfrac{2}{3}}(\sqrt[3]{b}-\sqrt[3]{b^{-2}})}\)
\(c)\ \dfrac{a^{\dfrac{1}{3}}b^{\dfrac{-1}{3}}-a^{\dfrac{-1}{3}}b^{\dfrac{1}{3}}}
{\sqrt[3]{a^2}-\sqrt[3]{b^2}}\)
\(d)\ \dfrac{a^{\dfrac{1}{3}} \sqrt{b}+b^{\dfrac{1}{3}} \sqrt{a}}
{\sqrt[6]{a}+\sqrt[6]{b}}\)
a)
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= ![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cfrac%7Ba%5E%7B1%7D+a%5E%7B2%7D%7D%7Ba%5E%7B1%7D+a%5E%7B0%7D%7D%3D%20%5Cfrac%7Ba%5Cleft%20%28%201+a%20%5Cright%20%29%7D%7Ba+1%7D%3D%20a)
b)
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. ( Với điều kiện b # 1)
c) \(\dfrac{a^{\dfrac{1}{3}}b^{-\dfrac{1}{3}-}a^{-\dfrac{1}{3}}b^{\dfrac{1}{3}}}{\sqrt[3]{a^2}-\sqrt[3]{b^2}}\)=
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( với điều kiện a#b).
d) \(\dfrac{a^{\dfrac{1}{3}}\sqrt{b}+b^{\dfrac{1}{3}}\sqrt{a}}{\sqrt[6]{a}+\sqrt[6]{b}}\) =
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= ![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?a%5E%7B%5Cfrac%7B2%7D%7B6%7D%7Db%5E%7B%5Cfrac%7B2%7D%7B6%7D%7D%20%3D%20a%5E%7B%5Cfrac%7B1%7D%7B3%7D%7Db%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%20%3D%20%5Csqrt%5B3%5D%7Bab%7D.)