פתור את 1000(1+.044/4)^48

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

הערך

$$1690.656849624850194676074036511614917659116760051199180877209172503884633043059911054094003552480084039488711419466290659533191490977168765017281$$

שלבי פתרון

הרחב את ‎\frac{0.044}{4} על-ידי הכפלת המונה והמכנה ב- 1000.

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

צמצם את השבר ‎\frac{44}{4000} לאיברים נמוכים יותר על-ידי ביטול 4.

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

חבר את ‎1 ו- ‎\frac{11}{1000} כדי לקבל ‎\frac{1011}{1000}.

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

חשב את \frac{1011}{1000} בחזקת 48 וקבל \frac{1690656849624850194676074036511614917659116760051199180877209172503884633043059911054094003552480084039488711419466290659533191490977168765017281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

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

הכפל את ‎1000 ו- ‎\frac{1690656849624850194676074036511614917659116760051199180877209172503884633043059911054094003552480084039488711419466290659533191490977168765017281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} כדי לקבל ‎\frac{1690656849624850194676074036511614917659116760051199180877209172503884633043059911054094003552480084039488711419466290659533191490977168765017281}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

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

פרק לגורמים

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