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

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

Calcula

$$\frac{3}{61035156250000000000000000000000000000000000}=4,9152 \cdot 10^{-44}$$

Passos de solució

Per elevar una potència a una altra potència, multipliqueu-ne els exponents. Multipliqueu 2 i -6 per obtenir -12.

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

Calculeu -27 elevat a 3 per obtenir -19683.

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

Calculeu 32 elevat a -5 per obtenir \frac{1}{33554432}.

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

Multipliqueu -19683 per \frac{1}{33554432} per obtenir -\frac{19683}{33554432}.

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

Calculeu -8 elevat a 5 per obtenir -32768.

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

Multipliqueu -\frac{19683}{33554432} per -32768 per obtenir \frac{19683}{1024}.

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

Calculeu 25 elevat a -12 per obtenir \frac{1}{59604644775390625}.

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

Multipliqueu \frac{19683}{1024} per \frac{1}{59604644775390625} per obtenir \frac{19683}{61035156250000000000}.

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

Calculeu -72 elevat a 4 per obtenir 26873856.

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

Calculeu 50 elevat a 3 per obtenir 125000.

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

Calculeu -125000 elevat a 4 per obtenir 244140625000000000000.

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

Multipliqueu 26873856 per 244140625000000000000 per obtenir 6561000000000000000000000000.

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

Expresseu \frac{\frac{19683}{61035156250000000000}}{6561000000000000000000000000} com a fracció senzilla.

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

Multipliqueu 61035156250000000000 per 6561000000000000000000000000 per obtenir 400451660156250000000000000000000000000000000000.

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

Redueix la fracció \frac{19683}{400451660156250000000000000000000000000000000000} al màxim extraient i anul·lant 6561.

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

Factoritzar

$$\frac{3}{2 ^ {34} \cdot 5 ^ {48}} = 4,9152000000000005 \times 10^{-44}$$