求解 1500000*(1+6/100)^30

$$1500000 \times ( 1 + \frac { 6 } { 100 } ) ^ { 30 }$$

求值

$$\frac{16047128959316527795784472485009960772040366899769947}{1862645149230957031250000000000000000000000000}=8615236.759369875$$

求解步骤

通过求根和消去 2，将分数 \frac{6}{100} 降低为最简分数。

$$1500000\left(1+\frac{3}{50}\right)^{30}$$

1 与 \frac{3}{50} 相加，得到 \frac{53}{50}。

$$1500000\times \left(\frac{53}{50}\right)^{30}$$

计算 30 的 \frac{53}{50} 乘方，得到 \frac{5349042986438842598594824161669986924013455633256649}{931322574615478515625000000000000000000000000000000}。

$$1500000\times \frac{5349042986438842598594824161669986924013455633256649}{931322574615478515625000000000000000000000000000000}$$

将 1500000 与 \frac{5349042986438842598594824161669986924013455633256649}{931322574615478515625000000000000000000000000000000} 相乘，得到 \frac{16047128959316527795784472485009960772040366899769947}{1862645149230957031250000000000000000000000000}。

$$\frac{16047128959316527795784472485009960772040366899769947}{1862645149230957031250000000000000000000000000}$$

因式分解

$$\frac{3 \cdot 53 ^ {30}}{2 ^ {25} \cdot 5 ^ {54}} = 8615236\frac{1.414436613662292 \times 10^{45}}{1.8626451492309573 \times 10^{45}} = 8615236.759369874$$