Solve (1/6)^20(1-1/6)^51-20

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

Evaluate

$$\frac{4656612873077392578125}{4849687664788584363858837602739217760256}\approx 9.601882008 \cdot 10^{-19}$$

Solution Steps

Calculate \frac{1}{6} to the power of 20 and get \frac{1}{3656158440062976}.

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

Subtract \frac{1}{6} from 1 to get \frac{5}{6}.

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

Subtract 20 from 51 to get 31.

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

Calculate \frac{5}{6} to the power of 31 and get \frac{4656612873077392578125}{1326443518324400147398656}.

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

Multiply \frac{1}{3656158440062976} and \frac{4656612873077392578125}{1326443518324400147398656} to get \frac{4656612873077392578125}{4849687664788584363858837602739217760256}.

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

Factor

$$\frac{5 ^ {31}}{2 ^ {51} \cdot 3 ^ {51}} = 9.60188200755067 \times 10^{-19}$$