簡約 8000[(1-(1.1)^{-8})/(0.1)]x(1.1)^{-9}

解

簡約

8000 [\frac{1 - ( 1.1 ) ^{- 8}}{0.1}] x (1.1)^{- 9}

18100.23595 \dots x

解答ステップ

8000 [\frac{1 - ( 1.1 ) ^{- 8}}{0.1}] x (1.1)^{- 9}

指数の規則を適用する:

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

= 8000 \cdot \frac{1}{1. 1 ^{9}} [\frac{1 - 1. 1 ^{- 8}}{0.1}] x

括弧を削除する:

(a) = a

= 8000 \cdot \frac{1 - 1. 1 ^{- 8}}{0.1} x \frac{1}{1. 1 ^{9}}

\frac{1 - 1. 1 ^{- 8}}{0.1} = \frac{0.53349 \dots}{0.1}

= 8000 \cdot \frac{1}{1. 1 ^{9}} \cdot \frac{0.53349 \dots}{0.1} x

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{0.53349 \dots \cdot 1 \cdot 8000 x}{0.1 \cdot 1. 1 ^{9}}

数を乗じる:

0.53349 \dots \cdot 1 \cdot 8000 = 4267.94095 \dots

= \frac{4267.94095 \dots x}{0.1 \cdot 1. 1 ^{9}}

0.1 \cdot 1. 1^{9} = 0.2357947691

= \frac{4267.94095 \dots x}{0.2357947691}

数を割る:

\frac{4267.94095 \dots}{0.2357947691} = 18100.23595 \dots

= 18100.23595 \dots x