求解 8000({left(1+.10/4right)}^4*8

$$8000( { \left(1+ \frac{ .10 }{ 4 } \right) }^{ 4 \times 8 }$$

求值

$$17630.055502182457021287162311143369465069400673479242842855985173855515313334763050079345703125$$

求解步骤

将分子和分母同时乘以 10 以展开 \frac{0.1}{4}。

$$8000\left(1+\frac{1}{40}\right)^{4\times 8}$$

1 与 \frac{1}{40} 相加，得到 \frac{41}{40}。

$$8000\times \left(\frac{41}{40}\right)^{4\times 8}$$

将 4 与 8 相乘，得到 32。

$$8000\times \left(\frac{41}{40}\right)^{32}$$

计算 32 的 \frac{41}{40} 乘方，得到 \frac{4065214023175683899921868126254722311886802750234881}{1844674407370955161600000000000000000000000000000000}。

$$8000\times \frac{4065214023175683899921868126254722311886802750234881}{1844674407370955161600000000000000000000000000000000}$$

将 8000 与 \frac{4065214023175683899921868126254722311886802750234881}{1844674407370955161600000000000000000000000000000000} 相乘，得到 \frac{4065214023175683899921868126254722311886802750234881}{230584300921369395200000000000000000000000000000}。

$$\frac{4065214023175683899921868126254722311886802750234881}{230584300921369395200000000000000000000000000000}$$

因式分解

$$\frac{41 ^ {32}}{2 ^ {90} \cdot 5 ^ {29}} = 17630\frac{1.2797931941781906 \times 10^{46}}{2.3058430092136937 \times 10^{47}} = 17630.05550218246$$