簡約 (b^{2/3}c^{2/5})(b^{4/9}c^{9/10})

解

簡約

(b^{\frac{2}{3}} \cdot c^{\frac{2}{5}}) (b^{\frac{4}{9}} \cdot c^{\frac{9}{10}})

b^{\frac{10}{9}} c^{\frac{13}{10}}

解答ステップ

(b^{\frac{2}{3}} c^{\frac{2}{5}}) (b^{\frac{4}{9}} c^{\frac{9}{10}})

指数の規則を適用する:

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

b^{\frac{2}{3}} b^{\frac{4}{9}} = b^{\frac{2}{3} + \frac{4}{9}}

= c^{\frac{2}{5}} b^{\frac{2}{3} + \frac{4}{9}} c^{\frac{9}{10}}

指数の規則を適用する:

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

c^{\frac{2}{5}} c^{\frac{9}{10}} = c^{\frac{2}{5} + \frac{9}{10}}

= b^{\frac{2}{3} + \frac{4}{9}} c^{\frac{2}{5} + \frac{9}{10}}

b^{\frac{2}{3} + \frac{4}{9}} = b^{\frac{10}{9}}

= b^{\frac{10}{9}} c^{\frac{2}{5} + \frac{9}{10}}

c^{\frac{2}{5} + \frac{9}{10}} = c^{\frac{13}{10}}

= b^{\frac{10}{9}} c^{\frac{13}{10}}