簡約 \sqrt[5]{sqrt((-1)/5)}

解

簡約

5 \frac{- 1}{5}

10 - 1 10 \frac{1}{5}

解答ステップ

5 \frac{- 1}{5}

累乗根の規則を適用する:

n a = a^{\frac{1}{n}}

= ((\frac{- 1}{5})^{\frac{1}{2}})^{\frac{1}{5}}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= (\frac{- 1}{5})^{\frac{1}{2} \cdot \frac{1}{5}}

\frac{1}{2} \cdot \frac{1}{5} = \frac{1}{10}

= (\frac{- 1}{5})^{\frac{1}{10}}

a^{\frac{1}{n}} = n a

= 10 \frac{- 1}{5}

分数の規則を適用する:

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

= 10 - \frac{1}{5}

累乗根の規則を適用する:

10 - a = 10 - 1 10 a

10 - \frac{1}{5} = 10 - 1 10 \frac{1}{5}

= 10 - 1 10 \frac{1}{5}