求解 500(1+0.7%)^40

$$500 ( 1 + 0.7 \% ) ^ { 40 }$$

求值

$$660.9198969602082479956572149866073342263871940426087708721362250985029258171259988778888826754136731390992510904624720005$$

求解步骤

将分子和分母同时乘以 10 以展开 \frac{0.7}{100}。

$$500\left(1+\frac{7}{1000}\right)^{40}$$

1 与 \frac{7}{1000} 相加，得到 \frac{1007}{1000}。

$$500\times \left(\frac{1007}{1000}\right)^{40}$$

计算 40 的 \frac{1007}{1000} 乘方，得到 \frac{1321839793920416495991314429973214668452774388085217541744272450197005851634251997755777765350827346278198502180924944001}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}。

$$500\times \frac{1321839793920416495991314429973214668452774388085217541744272450197005851634251997755777765350827346278198502180924944001}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

将 500 与 \frac{1321839793920416495991314429973214668452774388085217541744272450197005851634251997755777765350827346278198502180924944001}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} 相乘，得到 \frac{1321839793920416495991314429973214668452774388085217541744272450197005851634251997755777765350827346278198502180924944001}{2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}。

$$\frac{1321839793920416495991314429973214668452774388085217541744272450197005851634251997755777765350827346278198502180924944001}{2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

因式分解

$$\frac{19 ^ {40} \cdot 53 ^ {40}}{2 ^ {118} \cdot 5 ^ {117}} = 660\frac{1.8397939204166363 \times 10^{117}}{2 \times 10^{117}} = 660.9198969602083$$