Riješi (1/6)^20(1-1/6)^51-20

$$( 1 / 6 ) ^ { 20 } ( 1 - 1 / 6 ) ^ { 51 - 20 }$$

Procijeni

$$\frac{4656612873077392578125}{4849687664788584363858837602739217760256}\approx 9,601882008 \cdot 10^{-19}$$

Koraci za rješenje

Izračunajte \frac{1}{6} stepen od 20 i dobijte \frac{1}{3656158440062976}.

$$\frac{1}{3656158440062976}\left(1-\frac{1}{6}\right)^{51-20}$$

Oduzmite \frac{1}{6} od 1 da biste dobili \frac{5}{6}.

$$\frac{1}{3656158440062976}\times \left(\frac{5}{6}\right)^{51-20}$$

Oduzmite 20 od 51 da biste dobili 31.

$$\frac{1}{3656158440062976}\times \left(\frac{5}{6}\right)^{31}$$

Izračunajte \frac{5}{6} stepen od 31 i dobijte \frac{4656612873077392578125}{1326443518324400147398656}.

$$\frac{1}{3656158440062976}\times \frac{4656612873077392578125}{1326443518324400147398656}$$

Pomnožite \frac{1}{3656158440062976} i \frac{4656612873077392578125}{1326443518324400147398656} da biste dobili \frac{4656612873077392578125}{4849687664788584363858837602739217760256}.

$$\frac{4656612873077392578125}{4849687664788584363858837602739217760256}$$

Faktor

$$\frac{5 ^ {31}}{2 ^ {51} \cdot 3 ^ {51}} = 9,60188200755067 \times 10^{-19}$$