求解 4000(1+.044/4)^4(5)

$$4000 ( 1 + \frac { .044 } { 4 } ) ^ { 4 ( 5 ) }$$

求值

$$4978.323371133830101870227782125243658284214165724579503316804$$

求解步骤

将分子和分母同时乘以 1000 以展开 \frac{0.044}{4}。

$$4000\left(1+\frac{44}{4000}\right)^{4\times 5}$$

通过求根和消去 4，将分数 \frac{44}{4000} 降低为最简分数。

$$4000\left(1+\frac{11}{1000}\right)^{4\times 5}$$

1 与 \frac{11}{1000} 相加，得到 \frac{1011}{1000}。

$$4000\times \left(\frac{1011}{1000}\right)^{4\times 5}$$

将 4 与 5 相乘，得到 20。

$$4000\times \left(\frac{1011}{1000}\right)^{20}$$

计算 20 的 \frac{1011}{1000} 乘方，得到 \frac{1244580842783457525467556945531310914571053541431144875829201}{1000000000000000000000000000000000000000000000000000000000000}。

$$4000\times \frac{1244580842783457525467556945531310914571053541431144875829201}{1000000000000000000000000000000000000000000000000000000000000}$$

将 4000 与 \frac{1244580842783457525467556945531310914571053541431144875829201}{1000000000000000000000000000000000000000000000000000000000000} 相乘，得到 \frac{1244580842783457525467556945531310914571053541431144875829201}{250000000000000000000000000000000000000000000000000000000}。

$$\frac{1244580842783457525467556945531310914571053541431144875829201}{250000000000000000000000000000000000000000000000000000000}$$

因式分解

$$\frac{3 ^ {20} \cdot 337 ^ {20}}{2 ^ {55} \cdot 5 ^ {57}} = 4978\frac{8.084278345755884 \times 10^{55}}{2.5 \times 10^{56}} = 4978.32337113383$$