簡約 25(5*10^{-3}((e^{x/(0.026)})-1-2+x))

解

簡約

25 (5 \cdot 1 0^{- 3} ((e^{\frac{x}{0.026}}) - 1 - 2 + x))

\frac{x + e ^{\frac{x}{0.026}} - 3}{8}

解答ステップ

25 (5 \cdot 1 0^{- 3} ((e^{\frac{x}{0.026}}) - 1 - 2 + x))

指数の規則を適用する:

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

= 25 \cdot 5 \cdot \frac{1}{1 0 ^{3}} (x + e^{\frac{x}{0.026}} - 1 - 2)

分数を乗じる:

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

= \frac{1 \cdot 25 \cdot 5 ( e ^{\frac{x}{0.026}} - 1 - 2 + x )}{1 0 ^{3}}

1 \cdot 25 \cdot 5 (e^{\frac{x}{0.026}} - 1 - 2 + x) = 125 (x + e^{\frac{x}{0.026}} - 3)

= \frac{125 ( x + e ^{\frac{x}{0.026}} - 3 )}{1 0 ^{3}}

因数

125 : 5^{3}

因数

1 0^{3} : 2^{3} \cdot 5^{3}

= \frac{5 ^{3} ( x + e ^{\frac{x}{0.026}} - 3 )}{2 ^{3} \cdot 5 ^{3}}

共通因数を約分する:

5^{3}

= \frac{x + e ^{\frac{x}{0.026}} - 3}{2 ^{3}}

2^{3} = 8

= \frac{x + e ^{\frac{x}{0.026}} - 3}{8}