حل 1000(1+.044/4)^48

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

تقييم

$$1690.656849624850194676074036511614917659116760051199180877209172503884633043059911054094003552480084039488711419466290659533191490977168765017281$$

خطوات الحل

يمكنك توسيع \frac{0.044}{4} بضرب كل من البسط والمقام في 1000.

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

اختزل الكسر \frac{44}{4000} إلى أبسط قيمة من خلال استخراج 4 وشطبه.

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

اجمع 1 مع \frac{11}{1000} لتحصل على \frac{1011}{1000}.

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

احسب \frac{1011}{1000} بالأس 48 لتحصل على \frac{1690656849624850194676074036511614917659116760051199180877209172503884633043059911054094003552480084039488711419466290659533191490977168765017281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

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

اضرب 1000 في \frac{1690656849624850194676074036511614917659116760051199180877209172503884633043059911054094003552480084039488711419466290659533191490977168765017281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} لتحصل على \frac{1690656849624850194676074036511614917659116760051199180877209172503884633043059911054094003552480084039488711419466290659533191490977168765017281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

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

تحليل العوامل

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