簡約 (s^{2/5}t^{1/3})(s^{1/2}t^{1/2})

解

簡約

(s^{\frac{2}{5}} t^{\frac{1}{3}}) (s^{\frac{1}{2}} t^{\frac{1}{2}})

s^{\frac{9}{10}} t^{\frac{5}{6}}

解答ステップ

(s^{\frac{2}{5}} t^{\frac{1}{3}}) (s^{\frac{1}{2}} t^{\frac{1}{2}})

指数の規則を適用する:

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

s^{\frac{2}{5}} s^{\frac{1}{2}} = s^{\frac{2}{5} + \frac{1}{2}}

= t^{\frac{1}{3}} s^{\frac{2}{5} + \frac{1}{2}} t^{\frac{1}{2}}

指数の規則を適用する:

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

t^{\frac{1}{3}} t^{\frac{1}{2}} = t^{\frac{1}{3} + \frac{1}{2}}

= s^{\frac{2}{5} + \frac{1}{2}} t^{\frac{1}{3} + \frac{1}{2}}

s^{\frac{2}{5} + \frac{1}{2}} = s^{\frac{9}{10}}

= s^{\frac{9}{10}} t^{\frac{1}{3} + \frac{1}{2}}

t^{\frac{1}{3} + \frac{1}{2}} = t^{\frac{5}{6}}

= s^{\frac{9}{10}} t^{\frac{5}{6}}