簡約 (3^{1/5})/(\sqrt[5]{-96)}

解

簡約

\frac{3 ^{\frac{1}{5}}}{5 - 96}

- \frac{1}{2}

十進法表記

- 0.5

解答ステップ

\frac{3 ^{\frac{1}{5}}}{5 - 96}

指数の規則を適用する:

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

\frac{3 ^{\frac{1}{5}}}{5 - 96} = (\frac{3}{- 96})^{\frac{1}{5}}

= (\frac{3}{- 96})^{\frac{1}{5}}

\frac{3}{- 96} = - \frac{1}{32}

= (- \frac{1}{32})^{\frac{1}{5}}

指数の規則を適用する:

n

が奇数であれば,

(- a)^{\frac{1}{n}} = - (a)^{\frac{1}{n}}

(- \frac{1}{32})^{\frac{1}{5}} = - (\frac{1}{32})^{\frac{1}{5}}

= - (\frac{1}{32})^{\frac{1}{5}}

累乗根の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}},

, 以下を想定

a \geq 0, b \geq 0

(\frac{1}{32})^{\frac{1}{5}} = \frac{1 ^{\frac{1}{5}}}{3 2 ^{\frac{1}{5}}}

= - \frac{1 ^{\frac{1}{5}}}{3 2 ^{\frac{1}{5}}}

3 2^{\frac{1}{5}} = 2

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

規則を適用

1^{a} = 1

1^{\frac{1}{5}} = 1

= - \frac{1}{2}