簡約 (1/81)^{1/2}*(1/81)^{-3/4}

解

簡約

(\frac{1}{81})^{\frac{1}{2}} \cdot (\frac{1}{81})^{- \frac{3}{4}}

3

解答ステップ

(\frac{1}{81})^{\frac{1}{2}} (\frac{1}{81})^{- \frac{3}{4}}

指数の規則を適用する:

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

(\frac{1}{81})^{\frac{1}{2}} (\frac{1}{81})^{- \frac{3}{4}} = (\frac{1}{81})^{\frac{1}{2} - \frac{3}{4}}

= (\frac{1}{81})^{\frac{1}{2} - \frac{3}{4}}

\frac{1}{2} - \frac{3}{4} = - \frac{1}{4}

= (\frac{1}{81})^{- \frac{1}{4}}

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

(\frac{1}{81})^{- \frac{1}{4}} = \frac{1}{( \frac{1}{81} ) ^{\frac{1}{4}}}

= \frac{1}{( \frac{1}{81} ) ^{\frac{1}{4}}}

(\frac{1}{81})^{\frac{1}{4}} = \frac{1}{3}

= \frac{1}{\frac{1}{3}}

\frac{1}{\frac{1}{3}} = 3

= 3