因数 2(5a-1)^{3/4}+7a(5a-1)^{-1/4}

解

因数

2 (5 a - 1)^{\frac{3}{4}} + 7 a (5 a - 1)^{- \frac{1}{4}}

\frac{- 2 + 17 a}{( - 1 + 5 a ) ^{\frac{1}{4}}}

解答ステップ

2 (5 a - 1)^{\frac{3}{4}} + 7 a (5 a - 1)^{- \frac{1}{4}}

指数の規則を適用する:

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

(5 a - 1)^{\frac{3}{4}} = (5 a - 1)^{1 +- \frac{1}{4}} = (5 a - 1)^{1} (5 a - 1)^{- \frac{1}{4}}

= 2 (5 a - 1)^{1} (5 a - 1)^{- \frac{1}{4}} + 7 a (5 a - 1)^{- \frac{1}{4}}

共通項をくくり出す

(- 1 + 5 a)^{- \frac{1}{4}}

= (- 1 + 5 a)^{- \frac{1}{4}} (2 (- 1 + 5 a) + 7 a)

拡張

7 a + 2 (5 a - 1) : - 2 + 17 a

= (17 a - 2) (5 a - 1)^{- \frac{1}{4}}

改良

= \frac{17 a - 2}{( 5 a - 1 ) ^{\frac{1}{4}}}