Solve 8000(1+.085/4)^4(9)

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

Evaluate

$$17054.715946632433571754097095593005892745132495615410387216347292817838220759231113407893214190057999477600280547847994582465000605687251329645182096328426268883049488067626953125$$

Solution Steps

Expand \frac{0.085}{4} by multiplying both numerator and the denominator by 1000.

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

Reduce the fraction \frac{85}{4000} to lowest terms by extracting and canceling out 5.

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

Add 1 and \frac{17}{800} to get \frac{817}{800}.

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

Multiply 4 and 9 to get 36.

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

Calculate \frac{817}{800} to the power of 36 and get \frac{691821469007057920316493587021119081060434779266522946950218847647566909323782516160576296558710939916481}{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000}.

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

Multiply 8000 and \frac{691821469007057920316493587021119081060434779266522946950218847647566909323782516160576296558710939916481}{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{691821469007057920316493587021119081060434779266522946950218847647566909323782516160576296558710939916481}{40564819207303340847894502572032000000000000000000000000000000000000000000000000000000000000000000000}.

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

Factor

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