簡約 1000(1+(0.09)/(12))^{60}

解

簡約

1000 (1 + \frac{0.09}{12})^{60}

\frac{40 3 ^{60}}{2 ^{237} \cdot 5 ^{117}}

十進法表記

1565.68102 \dots

解答ステップ

1000 (1 + \frac{0.09}{12})^{60}

簡素化

1 + \frac{0.09}{12} : \frac{403}{400}

= 1000 (\frac{403}{400})^{60}

指数の規則を適用する:

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

(\frac{403}{400})^{60} = \frac{40 3 ^{60}}{40 0 ^{60}}

= 1000 \cdot \frac{40 3 ^{60}}{40 0 ^{60}}

1000 \cdot \frac{40 3 ^{60}}{40 0 ^{60}} = \frac{40 3 ^{60}}{2 ^{237} \cdot 5 ^{117}}

= \frac{40 3 ^{60}}{2 ^{237} \cdot 5 ^{117}}