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受欢迎的代数 >

化简 (2/3)^{2/3}*(3/2)^{-1/3}

解答

化简

(\frac{2}{3})^{\frac{2}{3}} \cdot (\frac{3}{2})^{- \frac{1}{3}}

解答

\frac{2}{3}

+1

十进制

0.66666 \dots

求解步骤

(\frac{2}{3})^{\frac{2}{3}} (\frac{3}{2})^{- \frac{1}{3}}

(\frac{2}{3})^{\frac{2}{3}} = (\frac{4}{9})^{\frac{1}{3}}

= (\frac{4}{9})^{\frac{1}{3}} (\frac{3}{2})^{- \frac{1}{3}}

(\frac{3}{2})^{- \frac{1}{3}} = (\frac{2}{3})^{\frac{1}{3}}

= (\frac{4}{9})^{\frac{1}{3}} (\frac{2}{3})^{\frac{1}{3}}

(\frac{4}{9})^{\frac{1}{3}} = (\frac{2}{3})^{\frac{2}{3}}

= (\frac{2}{3})^{\frac{2}{3}} (\frac{2}{3})^{\frac{1}{3}}

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

(\frac{2}{3})^{\frac{2}{3}} (\frac{2}{3})^{\frac{1}{3}} = (\frac{2}{3})^{\frac{2}{3} + \frac{1}{3}}

= (\frac{2}{3})^{\frac{2}{3} + \frac{1}{3}}

\frac{2}{3} + \frac{1}{3} = 1

= (\frac{2}{3})^{1}

使用指数法则:

a^{1} = a

= \frac{2}{3}

流行的例子

因式分解 4x+36