解決4000(1+.044/4)^4(5) |Microsoft數學求解器

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

評估

$$4978.323371133830101870227782125243658284214165724579503316804$$

解題步驟

同時對分子與分母乘上 1000 以展開 \frac{0.044}{4}。

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

透過找出與消去 4，對分式 \frac{44}{4000} 約分至最低項。

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

將 1 與 \frac{11}{1000} 相加可以得到 \frac{1011}{1000}。

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

將 4 乘上 5 得到 20。

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

計算 \frac{1011}{1000} 的 20 乘冪，然後得到 \frac{1244580842783457525467556945531310914571053541431144875829201}{1000000000000000000000000000000000000000000000000000000000000}。

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

將 4000 乘上 \frac{1244580842783457525467556945531310914571053541431144875829201}{1000000000000000000000000000000000000000000000000000000000000} 得到 \frac{1244580842783457525467556945531310914571053541431144875829201}{250000000000000000000000000000000000000000000000000000000}。

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

因式分解

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