Resolver 4!/4!*(4-0)!*{left(625/1296right)}^0*{left(1-625/1296right)}^4-0

$$\frac{ 4 ! }{ 4 ! \times (4-0) ! } \times { \left( \frac{ 625 }{ 1296 } \right) }^{ 0 } \times { \left(1- \frac{ 625 }{ 1296 } \right) }^{ 4-0 }$$

Calcular

$$\frac{202716958081}{67706637778944}\approx 0.002994049$$

Pasos da solución

O factor de 4 é 24.

$$\frac{24}{4!\left(4-0\right)!}\times \left(\frac{625}{1296}\right)^{0}\left(1-\frac{625}{1296}\right)^{4-0}$$

O factor de 4 é 24.

$$\frac{24}{24\left(4-0\right)!}\times \left(\frac{625}{1296}\right)^{0}\left(1-\frac{625}{1296}\right)^{4-0}$$

Resta 0 de 4 para obter 4.

$$\frac{24}{24\times 4!}\times \left(\frac{625}{1296}\right)^{0}\left(1-\frac{625}{1296}\right)^{4-0}$$

O factor de 4 é 24.

$$\frac{24}{24\times 24}\times \left(\frac{625}{1296}\right)^{0}\left(1-\frac{625}{1296}\right)^{4-0}$$

Multiplica 24 e 24 para obter 576.

$$\frac{24}{576}\times \left(\frac{625}{1296}\right)^{0}\left(1-\frac{625}{1296}\right)^{4-0}$$

Reduce a fracción \frac{24}{576} a termos máis baixos extraendo e cancelando 24.

$$\frac{1}{24}\times \left(\frac{625}{1296}\right)^{0}\left(1-\frac{625}{1296}\right)^{4-0}$$

Calcula \frac{625}{1296} á potencia de 0 e obtén 1.

$$\frac{1}{24}\times 1\left(1-\frac{625}{1296}\right)^{4-0}$$

Multiplica \frac{1}{24} e 1 para obter \frac{1}{24}.

$$\frac{1}{24}\left(1-\frac{625}{1296}\right)^{4-0}$$

Resta \frac{625}{1296} de 1 para obter \frac{671}{1296}.

$$\frac{1}{24}\times \left(\frac{671}{1296}\right)^{4-0}$$

Resta 0 de 4 para obter 4.

$$\frac{1}{24}\times \left(\frac{671}{1296}\right)^{4}$$

Calcula \frac{671}{1296} á potencia de 4 e obtén \frac{202716958081}{2821109907456}.

$$\frac{1}{24}\times \frac{202716958081}{2821109907456}$$

Multiplica \frac{1}{24} e \frac{202716958081}{2821109907456} para obter \frac{202716958081}{67706637778944}.

$$\frac{202716958081}{67706637778944}$$

Factorizar

$$\frac{11 ^ {4} \cdot 61 ^ {4}}{2 ^ {19} \cdot 3 ^ {17}} = 0.0029940485117995724$$