Løs 1-(1+8%)^-25/8%

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

Evaluer

$$\frac{6493111821791814823572418239644946025}{608266787713357709119683992618861307}\approx 10,674776189$$

Løsningsvejledning

Reducer fraktionen \frac{8}{100} til de laveste led ved at udtrække og annullere 4.

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

Tilføj 1 og \frac{2}{25} for at få \frac{27}{25}.

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

Beregn \frac{27}{25} til potensen af -25, og få \frac{88817841970012523233890533447265625}{608266787713357709119683992618861307}.

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

Subtraher \frac{88817841970012523233890533447265625}{608266787713357709119683992618861307} fra 1 for at få \frac{519448945743345185885793459171595682}{608266787713357709119683992618861307}.

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

Reducer fraktionen \frac{8}{100} til de laveste led ved at udtrække og annullere 4.

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

Divider \frac{519448945743345185885793459171595682}{608266787713357709119683992618861307} med \frac{2}{25} ved at multiplicere \frac{519448945743345185885793459171595682}{608266787713357709119683992618861307} med den reciprokke værdi af \frac{2}{25}.

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

Multiplicer \frac{519448945743345185885793459171595682}{608266787713357709119683992618861307} og \frac{25}{2} for at få \frac{6493111821791814823572418239644946025}{608266787713357709119683992618861307}.

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

Faktoriser

$$\frac{5 ^ {2} \cdot 11 \cdot 181 \cdot 1151 \cdot 5101 \cdot 22218307154177879570243101}{3 ^ {75}} = 10\frac{4,104439446582371 \times 10^{35}}{6,082667877133578 \times 10^{35}} = 10,674776188588577$$