حل 8000(1+.085/4)^4(9)

$$8000 ( 1 + \frac { .085 } { 4 } ) ^ { 4 ( 9 ) }$$

تقدير القيمة

$$17054.715946632433571754097095593005892745132495615410387216347292817838220759231113407893214190057999477600280547847994582465000605687251329645182096328426268883049488067626953125$$

خطوات الحل

يمكنك توسيع \frac{0.085}{4} بضرب كل من البسط والمقام في 1000.

$$8000\left(1+\frac{85}{4000}\right)^{4\times 9}$$

اختزل الكسر \frac{85}{4000} إلى أبسط قيمة من خلال استخراج 5 وشطبه.

$$8000\left(1+\frac{17}{800}\right)^{4\times 9}$$

اجمع 1 مع \frac{17}{800} لتحصل على \frac{817}{800}.

$$8000\times \left(\frac{817}{800}\right)^{4\times 9}$$

اضرب 4 في 9 لتحصل على 36.

$$8000\times \left(\frac{817}{800}\right)^{36}$$

احسب \frac{817}{800} بالأس 36 لتحصل على \frac{691821469007057920316493587021119081060434779266522946950218847647566909323782516160576296558710939916481}{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000}.

$$8000\times \frac{691821469007057920316493587021119081060434779266522946950218847647566909323782516160576296558710939916481}{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000}$$

اضرب 8000 في \frac{691821469007057920316493587021119081060434779266522946950218847647566909323782516160576296558710939916481}{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000} لتحصل على \frac{691821469007057920316493587021119081060434779266522946950218847647566909323782516160576296558710939916481}{40564819207303340847894502572032000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{691821469007057920316493587021119081060434779266522946950218847647566909323782516160576296558710939916481}{40564819207303340847894502572032000000000000000000000000000000000000000000000000000000000000000000000}$$

تحليل العوامل

$$\frac{19 ^ {36} \cdot 43 ^ {36}}{2 ^ {174} \cdot 5 ^ {69}} = 17054\frac{2.9042245706731613 \times 10^{100}}{4.056481920730334 \times 10^{100}} = 17054.715946632434$$