簡約 (v)(2x^2+3)^{5/3}(x+5)^{(-1)/2}

解

簡約

(v) \cdot (2 x^{2} + 3)^{\frac{5}{3}} \cdot (x + 5)^{\frac{- 1}{2}}

\frac{v ( 2 x ^{2} + 3 ) ^{\frac{5}{3}}}{( x + 5 ) ^{\frac{1}{2}}}

解答ステップ

(v) (2 x^{2} + 3)^{\frac{5}{3}} (x + 5)^{\frac{- 1}{2}}

規則を適用する:

(a) = a

(v) = v

= v (2 x^{2} + 3)^{\frac{5}{3}} (x + 5)^{\frac{- 1}{2}}

簡素化

(x + 5)^{\frac{- 1}{2}} : \frac{1}{( x + 5 ) ^{\frac{1}{2}}}

= v (2 x^{2} + 3)^{\frac{5}{3}} \frac{1}{( x + 5 ) ^{\frac{1}{2}}}

分数の規則を適用する:

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

= \frac{v ( 2 x ^{2} + 3 ) ^{\frac{5}{3}} \cdot 1}{( x + 5 ) ^{\frac{1}{2}}}

規則を適用する:

a \cdot 1 = a

v (2 x^{2} + 3)^{\frac{5}{3}} \cdot 1 = v (2 x^{2} + 3)^{\frac{5}{3}}

= \frac{v ( 2 x ^{2} + 3 ) ^{\frac{5}{3}}}{( x + 5 ) ^{\frac{1}{2}}}