Løs 5!/49!*2!

$$\frac{ 5 ! }{ 49 ! \times 2 ! }$$

Evaluer

$$\frac{1}{10138031067237792681204202722021589614792547189653504000000000}\approx 9,86384825 \cdot 10^{-62}$$

Løsningsvejledning

Fakulteten af 5 er 120.

$$\frac{120}{49!\times 2!}$$

Fakulteten af 49 er 608281864034267560872252163321295376887552831379210240000000000.

$$\frac{120}{608281864034267560872252163321295376887552831379210240000000000\times 2!}$$

Fakulteten af 2 er 2.

$$\frac{120}{608281864034267560872252163321295376887552831379210240000000000\times 2}$$

Multiplicer 608281864034267560872252163321295376887552831379210240000000000 og 2 for at få 1216563728068535121744504326642590753775105662758420480000000000.

$$\frac{120}{1216563728068535121744504326642590753775105662758420480000000000}$$

Reducer fraktionen \frac{120}{1216563728068535121744504326642590753775105662758420480000000000} til de laveste led ved at udtrække og annullere 120.

$$\frac{1}{10138031067237792681204202722021589614792547189653504000000000}$$

Faktoriser

$$\frac{1}{2 ^ {44} \cdot 3 ^ {21} \cdot 5 ^ {9} \cdot 7 ^ {8} \cdot 11 ^ {4} \cdot 13 ^ {3} \cdot 17 ^ {2} \cdot 19 ^ {2} \cdot 23 ^ {2} \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \cdot 47} = 9,863848249899473 \times 10^{-62}$$