簡約 3^{5/6}*243^{5/6}

解

簡約

3^{\frac{5}{6}} \cdot 24 3^{\frac{5}{6}}

243

解答ステップ

3^{\frac{5}{6}} \cdot 24 3^{\frac{5}{6}}

指数の規則を適用する:

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

3^{\frac{5}{6}} \cdot 24 3^{\frac{5}{6}} = (3 \cdot 243)^{\frac{5}{6}}

= (3 \cdot 243)^{\frac{5}{6}}

数を乗じる:

3 \cdot 243 = 729

= 72 9^{\frac{5}{6}}

数を因数に分解する:

729 = 3^{6}

= (3^{6})^{\frac{5}{6}}

指数の規則を適用する:

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

(3^{6})^{\frac{5}{6}} = 3^{6 \cdot \frac{5}{6}} = 3^{5}

= 3^{5}

改良

= 243