簡約 18000((1-1.1^{-11})/(0.1))(1.1^{-19})

解

簡約

18000 (\frac{1 - 1. 1 ^{- 11}}{0.1}) (1. 1^{- 19})

19115.89875 \dots

解答ステップ

18000 (\frac{1 - 1. 1 ^{- 11}}{0.1}) (1. 1^{- 19})

指数の規則を適用する:

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

= 18000 \cdot \frac{1}{1. 1 ^{19}} \cdot \frac{1 - 1. 1 ^{- 11}}{0.1}

\frac{1 - 1. 1 ^{- 11}}{0.1} = \frac{0.64950 \dots}{0.1}

= 18000 \cdot \frac{1}{1. 1 ^{19}} \cdot \frac{0.64950 \dots}{0.1}

分数を乗じる:

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

= \frac{0.64950 \dots \cdot 1 \cdot 18000}{0.1 \cdot 1. 1 ^{19}}

数を乗じる:

0.64950 \dots \cdot 1 \cdot 18000 = 11691.10980 \dots

= \frac{11691.10980 \dots}{0.1 \cdot 1. 1 ^{19}}

0.1 \cdot 1. 1^{19} = 0.61159 \dots

= \frac{11691.10980 \dots}{0.61159 \dots}

数を割る:

\frac{11691.10980 \dots}{0.61159 \dots} = 19115.89875 \dots

= 19115.89875 \dots