簡約 ((c^4d^{-3})/(c^7d^5))^{1/4}

解

簡約

(\frac{c ^{4} d ^{- 3}}{c ^{7} d ^{5}})^{\frac{1}{4}}

\frac{1}{d ^{2} c ^{\frac{3}{4}}}

解答ステップ

(\frac{c ^{4} d ^{- 3}}{c ^{7} d ^{5}})^{\frac{1}{4}}

指数の規則を適用する:

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

= \frac{( c ^{4} d ^{- 3} ) ^{\frac{1}{4}}}{( c ^{7} d ^{5} ) ^{\frac{1}{4}}}

簡素化

(c^{4} d^{- 3})^{\frac{1}{4}} : \frac{c}{d ^{\frac{3}{4}}}

= \frac{\frac{c}{d ^{\frac{3}{4}}}}{( c ^{7} d ^{5} ) ^{\frac{1}{4}}}

簡素化

(c^{7} d^{5})^{\frac{1}{4}} : c^{\frac{7}{4}} d^{\frac{5}{4}}

= \frac{\frac{c}{d ^{\frac{3}{4}}}}{c ^{\frac{7}{4}} d ^{\frac{5}{4}}}

分数の規則を適用する:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{c}{d ^{\frac{3}{4}} c ^{\frac{7}{4}} d ^{\frac{5}{4}}}

指数の規則を適用する:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{c}{c ^{\frac{7}{4}}} = \frac{1}{c ^{\frac{7}{4} - 1}}

= \frac{1}{d ^{\frac{3}{4}} d ^{\frac{5}{4}} c ^{\frac{7}{4} - 1}}

数を引く:

\frac{7}{4} - 1 = \frac{3}{4}

= \frac{1}{c ^{\frac{3}{4}} d ^{\frac{3}{4}} d ^{\frac{5}{4}}}

c^{\frac{3}{4}} d^{\frac{3}{4}} d^{\frac{5}{4}} = c^{\frac{3}{4}} d^{\frac{3}{4} + \frac{5}{4}}

= \frac{1}{c ^{\frac{3}{4}} d ^{\frac{3}{4} + \frac{5}{4}}}

分数を組み合わせる

\frac{3}{4} + \frac{5}{4} : 2

= \frac{1}{d ^{2} c ^{\frac{3}{4}}}