簡約 (m^{5/4}n^{-4/5})^{7/3}

解

簡約

(m^{\frac{5}{4}} n^{- \frac{4}{5}})^{\frac{7}{3}}

\frac{m ^{\frac{35}{12}}}{n ^{\frac{28}{15}}}

解答ステップ

(m^{\frac{5}{4}} n^{- \frac{4}{5}})^{\frac{7}{3}}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

(m^{\frac{5}{4}} n^{- \frac{4}{5}})^{\frac{7}{3}} = (m^{\frac{5}{4}})^{\frac{7}{3}} (n^{- \frac{4}{5}})^{\frac{7}{3}}

= (m^{\frac{5}{4}})^{\frac{7}{3}} (n^{- \frac{4}{5}})^{\frac{7}{3}}

簡素化

(m^{\frac{5}{4}})^{\frac{7}{3}} : m^{\frac{35}{12}}

= m^{\frac{35}{12}} (n^{- \frac{4}{5}})^{\frac{7}{3}}

簡素化

(n^{- \frac{4}{5}})^{\frac{7}{3}} : \frac{1}{n ^{\frac{28}{15}}}

= m^{\frac{35}{12}} \frac{1}{n ^{\frac{28}{15}}}

簡素化

m^{\frac{35}{12}} \frac{1}{n ^{\frac{28}{15}}} : \frac{m ^{\frac{35}{12}}}{n ^{\frac{28}{15}}}

= \frac{m ^{\frac{35}{12}}}{n ^{\frac{28}{15}}}