簡約 (1.01^{365})/(0.99^{365)}

解

簡約

\frac{1.0 1 ^{365}}{0.9 9 ^{365}}

1480.66019 \dots

解答ステップ

\frac{1.0 1 ^{365}}{0.9 9 ^{365}}

指数の規則を適用する:

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

\frac{1.0 1 ^{365}}{0.9 9 ^{365}} = (\frac{1.01}{0.99})^{365}

= (\frac{1.01}{0.99})^{365}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1.0 1 ^{365}}{0.9 9 ^{365}}

1.0 1^{365} = 37.78343 \dots

= \frac{37.78343 \dots}{0.9 9 ^{365}}

0.9 9^{365} = 0.02551 \dots

= \frac{37.78343 \dots}{0.02551 \dots}

数を割る:

\frac{37.78343 \dots}{0.02551 \dots} = 1480.66019 \dots

= 1480.66019 \dots