簡約 5^{1/5}((-1)^{2/(5pi)})^{1/5}

解

簡約

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

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

解答ステップ

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

指数の規則を適用する:

a^{m} b^{m} = (ab)^{m},

, 以下を想定

a \geq 0, b \geq 0

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

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

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

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