簡約 1000(1+(0.02)/4)^{(4*8)}

解

簡約

1000 (1 + \frac{0.02}{4})^{(4 \cdot 8)}

\frac{20 1 ^{32}}{5 ^{61} \cdot 8 ^{31}}

十進法表記

1173.04311 \dots

解答ステップ

1000 (1 + \frac{0.02}{4})^{4 \cdot 8}

数を乗じる:

4 \cdot 8 = 32

= 1000 (1 + \frac{0.02}{4})^{32}

簡素化

1 + \frac{0.02}{4} : \frac{201}{200}

= 1000 (\frac{201}{200})^{32}

指数の規則を適用する:

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

(\frac{201}{200})^{32} = \frac{20 1 ^{32}}{20 0 ^{32}}

= 1000 \cdot \frac{20 1 ^{32}}{20 0 ^{32}}

1000 \cdot \frac{20 1 ^{32}}{20 0 ^{32}} = \frac{20 1 ^{32}}{5 ^{61} \cdot 8 ^{31}}

= \frac{20 1 ^{32}}{5 ^{61} \cdot 8 ^{31}}