求解 8000(1+.085/4)^4(9)

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

求值

$$17054.715946632433571754097095593005892745132495615410387216347292817838220759231113407893214190057999477600280547847994582465000605687251329645182096328426268883049488067626953125$$

求解步骤

将分子和分母同时乘以 1000 以展开 \frac{0.085}{4}。

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

通过求根和消去 5，将分数 \frac{85}{4000} 降低为最简分数。

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

1 与 \frac{17}{800} 相加，得到 \frac{817}{800}。

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

将 4 与 9 相乘，得到 36。

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

计算 36 的 \frac{817}{800} 乘方，得到 \frac{691821469007057920316493587021119081060434779266522946950218847647566909323782516160576296558710939916481}{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000}。

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

将 8000 与 \frac{691821469007057920316493587021119081060434779266522946950218847647566909323782516160576296558710939916481}{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000} 相乘，得到 \frac{691821469007057920316493587021119081060434779266522946950218847647566909323782516160576296558710939916481}{40564819207303340847894502572032000000000000000000000000000000000000000000000000000000000000000000000}。

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

因式分解

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