Question

8．已知a，b∈R⁺，則$\frac{{\sqrt{{a^3}b}}}{{\root{3}{ab}}}$=（　�。�

• A． ${a^{\frac{1}{6}}}{b^{\frac{7}{6}}}$
• B． ${a^{\frac{7}{6}}}{b^{\frac{1}{6}}}$
• C． ${a^{\frac{1}{3}}}{b^{\frac{1}{6}}}$
• D． ${a^{\frac{1}{2}}}{b^{\frac{1}{6}}}$

Answer 1

分析 利用根式與分數(shù)指數(shù)冪化簡$\frac{{\sqrt{{a^3}b}}}{{\root{3}{ab}}}$=$\frac{{a}^{\frac{3}{2}}^{\frac{1}{2}}}{{a}^{\frac{1}{3}}^{\frac{1}{3}}}$=${a}^{\frac{3}{2}-\frac{1}{3}}$$^{\frac{1}{2}-\frac{1}{3}}$，從而解得．

解答 解：$\frac{{\sqrt{{a^3}b}}}{{\root{3}{ab}}}$=$\frac{{a}^{\frac{3}{2}}^{\frac{1}{2}}}{{a}^{\frac{1}{3}}^{\frac{1}{3}}}$
=${a}^{\frac{3}{2}-\frac{1}{3}}$$^{\frac{1}{2}-\frac{1}{3}}$
=${a^{\frac{7}{6}}}{b^{\frac{1}{6}}}$，
故選B．

點評 本題考查了根式與分數(shù)指數(shù)冪的互化．