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Evaluate the following expression: $$\left(\sqrt[3]{1+2\sqrt{6}}-\sqrt[6]{25+4\sqrt{6}}\right)\xb7\sqrt[3]{2\sqrt{6}-1}$$ |

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Simplify the following expression: $${x}^{\frac{2}{3}}\xb7{x}^{\frac{3}{4}}\xb7{x}^{-1}$$ |

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Evaluate the following expression: $$\sqrt{6-4\sqrt{2}}$$ |

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Evaluate the following expression: $${243}^{\frac{1}{5}}-{\left(\frac{1}{81}\right)}^{\frac{1}{4}}+{\left(92+7,5\right)}^{0}+{\left({9}^{\frac{7}{8}}:{3}^{\frac{5}{4}}\right)}^{4}$$ |

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Prove the truth of equation below. $$\sqrt[3]{\frac{{a}^{2}}{b}}\xb7\sqrt[4]{\frac{3{b}^{3}}{5{a}^{3}}}\xb7\sqrt[6]{\frac{5a}{3{b}^{3}}}=\sqrt[8]{\frac{{a}^{2}}{2b}}\xb7\sqrt[12]{\frac{3{b}^{2}}{{a}^{2}}}\xb7\sqrt[24]{\frac{8}{25{b}^{3}}}$$ |

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Solve the following equation. $$\frac{{\left(\sqrt{a}-\sqrt{b}\right)}^{3}+2\sqrt{{a}^{3}}+b\sqrt{b}}{a\sqrt{a}+b\sqrt{b}}+\frac{3\sqrt{ab}-b}{a-b}a>0;b0$$ |

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Simplify the following expression: $$\sqrt{\frac{\left(1+a\right)\xb7\sqrt[3]{1+a}}{3a}}\xb7\sqrt[3]{\frac{\sqrt{3}}{9+18{a}^{-1}+9{a}^{-2}}}$$ |

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Simplify the following expression: $$a\sqrt{128}$$ |

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Simplify the following expression: $$\sqrt{ab}\xb7\sqrt[6]{{a}^{2}{b}^{3}}\xb7\sqrt[6]{{a}^{9}{b}^{8}}$$ |