Resolver frac{(-27)^{3}(32)^{-2}(-8)^{4}(25^2)}{(-72)^4(-50^3)^4}

$$\frac { ( - 27 ) ^ { 3 } ( 32 ) ^ { - 2 } ( - 8 ) ^ { 4 } ( 25 ^ { 2 } ) } { ( - 72 ) ^ { 4 } ( - 50 ^ { 3 } ) ^ { 4 } }$$

Calcular

$$-\frac{3}{400000000000000000000}=-7.5 \cdot 10^{-21}$$

Pasos da solución

Calcula -27 á potencia de 3 e obtén -19683.

$$\frac{-19683\times 32^{-2}\left(-8\right)^{4}\times 25^{2}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Calcula 32 á potencia de -2 e obtén \frac{1}{1024}.

$$\frac{-19683\times \frac{1}{1024}\left(-8\right)^{4}\times 25^{2}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Multiplica -19683 e \frac{1}{1024} para obter -\frac{19683}{1024}.

$$\frac{-\frac{19683}{1024}\left(-8\right)^{4}\times 25^{2}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Calcula -8 á potencia de 4 e obtén 4096.

$$\frac{-\frac{19683}{1024}\times 4096\times 25^{2}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Multiplica -\frac{19683}{1024} e 4096 para obter -78732.

$$\frac{-78732\times 25^{2}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Calcula 25 á potencia de 2 e obtén 625.

$$\frac{-78732\times 625}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Multiplica -78732 e 625 para obter -49207500.

$$\frac{-49207500}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Calcula -72 á potencia de 4 e obtén 26873856.

$$\frac{-49207500}{26873856\left(-50^{3}\right)^{4}}$$

Calcula 50 á potencia de 3 e obtén 125000.

$$\frac{-49207500}{26873856\left(-125000\right)^{4}}$$

Calcula -125000 á potencia de 4 e obtén 244140625000000000000.

$$\frac{-49207500}{26873856\times 244140625000000000000}$$

Multiplica 26873856 e 244140625000000000000 para obter 6561000000000000000000000000.

$$\frac{-49207500}{6561000000000000000000000000}$$

Reduce a fracción \frac{-49207500}{6561000000000000000000000000} a termos máis baixos extraendo e cancelando 16402500.

$$-\frac{3}{400000000000000000000}$$

Factorizar

$$-\frac{3}{400000000000000000000} = -7.500000000000002 \times 10^{-21}$$