簡約 2*243^{4/5}

解

簡約

2 \cdot 24 3^{\frac{4}{5}}

162

解答ステップ

2 \cdot 24 3^{\frac{4}{5}}

数を因数に分解する:

243 = 3^{5}

= 2 (3^{5})^{\frac{4}{5}}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}, a \geq 0

(3^{5})^{\frac{4}{5}} = 3^{5 \cdot \frac{4}{5}}

= 2 \cdot 3^{5 \cdot \frac{4}{5}}

5 \cdot \frac{4}{5} = 4

= 2 \cdot 3^{4}

3^{4} = 81

= 2 \cdot 81

数を乗じる:

2 \cdot 81 = 162

= 162