簡約 243^{7/10}*243^{1/10}

解

簡約

24 3^{\frac{7}{10}} \cdot 24 3^{\frac{1}{10}}

81

解答ステップ

24 3^{\frac{7}{10}} \cdot 24 3^{\frac{1}{10}}

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

24 3^{\frac{7}{10}} \cdot 24 3^{\frac{1}{10}} = 24 3^{\frac{7}{10} + \frac{1}{10}}

= 24 3^{\frac{7}{10} + \frac{1}{10}}

\frac{7}{10} + \frac{1}{10} = \frac{4}{5}

= 24 3^{\frac{4}{5}}

数を因数に分解する:

243 = 3^{5}

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

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

= 3^{4}

3^{4} = 81

= 81