求解 1000(1+.044/4)^48

$$1000 ( 1 + \frac { .044 } { 4 } ) ^ { 48 }$$

求值

$$1690.656849624850194676074036511614917659116760051199180877209172503884633043059911054094003552480084039488711419466290659533191490977168765017281$$

求解步骤

将分子和分母同时乘以 1000 以展开 \frac{0.044}{4}。

$$1000\left(1+\frac{44}{4000}\right)^{48}$$

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

$$1000\left(1+\frac{11}{1000}\right)^{48}$$

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

$$1000\times \left(\frac{1011}{1000}\right)^{48}$$

计算 48 的 \frac{1011}{1000} 乘方，得到 \frac{1690656849624850194676074036511614917659116760051199180877209172503884633043059911054094003552480084039488711419466290659533191490977168765017281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}。

$$1000\times \frac{1690656849624850194676074036511614917659116760051199180877209172503884633043059911054094003552480084039488711419466290659533191490977168765017281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

将 1000 与 \frac{1690656849624850194676074036511614917659116760051199180877209172503884633043059911054094003552480084039488711419466290659533191490977168765017281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} 相乘，得到 \frac{1690656849624850194676074036511614917659116760051199180877209172503884633043059911054094003552480084039488711419466290659533191490977168765017281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}。

$$\frac{1690656849624850194676074036511614917659116760051199180877209172503884633043059911054094003552480084039488711419466290659533191490977168765017281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

因式分解

$$\frac{3 ^ {48} \cdot 337 ^ {48}}{2 ^ {141} \cdot 5 ^ {141}} = 1690\frac{6.568496248504368 \times 10^{140}}{1 \times 10^{141}} = 1690.6568496248503$$