Riješi (20*19)^5/100*99*98*97*96*95*94*93*92*91

$$\frac { ( 20 \times 19 ) ^ { 5 } } { 100 \times 99 \times 98 \times 97 \times 96 \times 95 \times 94 \times 93 \times 92 \times 91 }$$

Procijeni

$$\frac{3258025}{25828803846846}\approx 0,000000126$$

Koraci za rješenje

Pomnožite 20 i 19 da biste dobili 380.

$$\frac{380^{5}}{100\times 99\times 98\times 97\times 96\times 95\times 94\times 93\times 92\times 91}$$

Izračunajte 380 stepen od 5 i dobijte 7923516800000.

$$\frac{7923516800000}{100\times 99\times 98\times 97\times 96\times 95\times 94\times 93\times 92\times 91}$$

Pomnožite 100 i 99 da biste dobili 9900.

$$\frac{7923516800000}{9900\times 98\times 97\times 96\times 95\times 94\times 93\times 92\times 91}$$

Pomnožite 9900 i 98 da biste dobili 970200.

$$\frac{7923516800000}{970200\times 97\times 96\times 95\times 94\times 93\times 92\times 91}$$

Pomnožite 970200 i 97 da biste dobili 94109400.

$$\frac{7923516800000}{94109400\times 96\times 95\times 94\times 93\times 92\times 91}$$

Pomnožite 94109400 i 96 da biste dobili 9034502400.

$$\frac{7923516800000}{9034502400\times 95\times 94\times 93\times 92\times 91}$$

Pomnožite 9034502400 i 95 da biste dobili 858277728000.

$$\frac{7923516800000}{858277728000\times 94\times 93\times 92\times 91}$$

Pomnožite 858277728000 i 94 da biste dobili 80678106432000.

$$\frac{7923516800000}{80678106432000\times 93\times 92\times 91}$$

Pomnožite 80678106432000 i 93 da biste dobili 7503063898176000.

$$\frac{7923516800000}{7503063898176000\times 92\times 91}$$

Pomnožite 7503063898176000 i 92 da biste dobili 690281878632192000.

$$\frac{7923516800000}{690281878632192000\times 91}$$

Pomnožite 690281878632192000 i 91 da biste dobili 62815650955529472000.

$$\frac{7923516800000}{62815650955529472000}$$

Svedite razlomak \frac{7923516800000}{62815650955529472000} na najprostije elemente rastavlјanjem i kraćenjem 2432000.

$$\frac{3258025}{25828803846846}$$

Faktor

$$\frac{5 ^ {2} \cdot 19 ^ {4}}{2 \cdot 3 ^ {4} \cdot 7 ^ {3} \cdot 11 \cdot 13 \cdot 23 \cdot 31 \cdot 47 \cdot 97} = 1,261392133882283 \times 10^{-7}$$