Solve 1-(1+8%)^-25/8%

$$\frac { 1 - ( 1 + 8 \% ) ^ { - 25 } } { 8 \% }$$

Evaluate

$$\frac{6493111821791814823572418239644946025}{608266787713357709119683992618861307}\approx 10.674776189$$

Solution Steps

Reduce the fraction \frac{8}{100} to lowest terms by extracting and canceling out 4.

$$\frac{1-\left(1+\frac{2}{25}\right)^{-25}}{\frac{8}{100}}$$

Add 1 and \frac{2}{25} to get \frac{27}{25}.

$$\frac{1-\left(\frac{27}{25}\right)^{-25}}{\frac{8}{100}}$$

Calculate \frac{27}{25} to the power of -25 and get \frac{88817841970012523233890533447265625}{608266787713357709119683992618861307}.

$$\frac{1-\frac{88817841970012523233890533447265625}{608266787713357709119683992618861307}}{\frac{8}{100}}$$

Subtract \frac{88817841970012523233890533447265625}{608266787713357709119683992618861307} from 1 to get \frac{519448945743345185885793459171595682}{608266787713357709119683992618861307}.

$$\frac{\frac{519448945743345185885793459171595682}{608266787713357709119683992618861307}}{\frac{8}{100}}$$

Reduce the fraction \frac{8}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{519448945743345185885793459171595682}{608266787713357709119683992618861307}}{\frac{2}{25}}$$

Divide \frac{519448945743345185885793459171595682}{608266787713357709119683992618861307} by \frac{2}{25} by multiplying \frac{519448945743345185885793459171595682}{608266787713357709119683992618861307} by the reciprocal of \frac{2}{25}.

$$\frac{519448945743345185885793459171595682}{608266787713357709119683992618861307}\times \frac{25}{2}$$

Multiply \frac{519448945743345185885793459171595682}{608266787713357709119683992618861307} and \frac{25}{2} to get \frac{6493111821791814823572418239644946025}{608266787713357709119683992618861307}.

$$\frac{6493111821791814823572418239644946025}{608266787713357709119683992618861307}$$

Factor

$$\frac{5 ^ {2} \cdot 11 \cdot 181 \cdot 1151 \cdot 5101 \cdot 22218307154177879570243101}{3 ^ {75}} = 10\frac{4.104439446582371 \times 10^{35}}{6.082667877133578 \times 10^{35}} = 10.674776188588577$$