簡約 (16x^{16})^{1/4}

解

簡約

(16 x^{16})^{\frac{1}{4}}

2 x^{4}

解答ステップ

(16 x^{16})^{\frac{1}{4}}

指数の規則を適用する:

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

(16 x^{16})^{\frac{1}{4}} = 1 6^{\frac{1}{4}} (x^{16})^{\frac{1}{4}}

= 1 6^{\frac{1}{4}} (x^{16})^{\frac{1}{4}}

1 6^{\frac{1}{4}} = 2

= 2 (x^{16})^{\frac{1}{4}}

指数の規則を適用する:

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

, 以下を想定

a \geq 0

(x^{16})^{\frac{1}{4}} = x^{16 \cdot \frac{1}{4}}

= 2 x^{16 \cdot \frac{1}{4}}

16 \cdot \frac{1}{4} = 4

= 2 x^{4}