Resolver frac{(-27)^{3}(32)^{-5}(-8)^{5}(25^{2})^-6}{(-72)^4(-50^3)^4}

$$\frac { ( - 27 ) ^ { 3 } ( 32 ) ^ { - 5 } ( - 8 ) ^ { 5 } ( 25 ^ { 2 } ) ^ { - 6 } } { ( - 72 ) ^ { 4 } ( - 50 ^ { 3 } ) ^ { 4 } }$$

Calcular

$$\frac{3}{61035156250000000000000000000000000000000000}=4.9152 \cdot 10^{-44}$$

Pasos da solución

Para elevar unha potencia a outra potencia, multiplica os expoñentes. Multiplica 2 e -6 para obter -12.

$$\frac{\left(-27\right)^{3}\times 32^{-5}\left(-8\right)^{5}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

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

$$\frac{-19683\times 32^{-5}\left(-8\right)^{5}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Calcula 32 á potencia de -5 e obtén \frac{1}{33554432}.

$$\frac{-19683\times \frac{1}{33554432}\left(-8\right)^{5}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Multiplica -19683 e \frac{1}{33554432} para obter -\frac{19683}{33554432}.

$$\frac{-\frac{19683}{33554432}\left(-8\right)^{5}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Calcula -8 á potencia de 5 e obtén -32768.

$$\frac{-\frac{19683}{33554432}\left(-32768\right)\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Multiplica -\frac{19683}{33554432} e -32768 para obter \frac{19683}{1024}.

$$\frac{\frac{19683}{1024}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Calcula 25 á potencia de -12 e obtén \frac{1}{59604644775390625}.

$$\frac{\frac{19683}{1024}\times \frac{1}{59604644775390625}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Multiplica \frac{19683}{1024} e \frac{1}{59604644775390625} para obter \frac{19683}{61035156250000000000}.

$$\frac{\frac{19683}{61035156250000000000}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Calcula -72 á potencia de 4 e obtén 26873856.

$$\frac{\frac{19683}{61035156250000000000}}{26873856\left(-50^{3}\right)^{4}}$$

Calcula 50 á potencia de 3 e obtén 125000.

$$\frac{\frac{19683}{61035156250000000000}}{26873856\left(-125000\right)^{4}}$$

Calcula -125000 á potencia de 4 e obtén 244140625000000000000.

$$\frac{\frac{19683}{61035156250000000000}}{26873856\times 244140625000000000000}$$

Multiplica 26873856 e 244140625000000000000 para obter 6561000000000000000000000000.

$$\frac{\frac{19683}{61035156250000000000}}{6561000000000000000000000000}$$

Expresa \frac{\frac{19683}{61035156250000000000}}{6561000000000000000000000000} como unha única fracción.

$$\frac{19683}{61035156250000000000\times 6561000000000000000000000000}$$

Multiplica 61035156250000000000 e 6561000000000000000000000000 para obter 400451660156250000000000000000000000000000000000.

$$\frac{19683}{400451660156250000000000000000000000000000000000}$$

Reduce a fracción \frac{19683}{400451660156250000000000000000000000000000000000} a termos máis baixos extraendo e cancelando 6561.

$$\frac{3}{61035156250000000000000000000000000000000000}$$

Factorizar

$$\frac{3}{2 ^ {34} \cdot 5 ^ {48}} = 4.9152000000000005 \times 10^{-44}$$