Resolver frac{-27^332^-5-8^5{left(25^2right)}^-6}{{-72}^4{left(-{50}^3right)}^4}

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

Avaliar

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

Passos Para a Resolução

Para aumentar uma potência para outra potência, multiplique os expoentes. Multiplique 2 e -6 para obter -12.

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

Calcule -27 elevado a 3 e obtenha -19683.

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

Calcule 32 elevado a -5 e obtenha \frac{1}{33554432}.

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

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

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

Calcule -8 elevado a 5 e obtenha -32768.

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

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

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

Calcule 25 elevado a -12 e obtenha \frac{1}{59604644775390625}.

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

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

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

Calcule -72 elevado a 4 e obtenha 26873856.

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

Calcule 50 elevado a 3 e obtenha 125000.

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

Calcule -125000 elevado a 4 e obtenha 244140625000000000000.

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

Multiplique 26873856 e 244140625000000000000 para obter 6561000000000000000000000000.

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

Expresse \frac{\frac{19683}{61035156250000000000}}{6561000000000000000000000000} como uma fração única.

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

Multiplique 61035156250000000000 e 6561000000000000000000000000 para obter 400451660156250000000000000000000000000000000000.

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

Reduza a fração \frac{19683}{400451660156250000000000000000000000000000000000} para os termos mais baixos ao retirar e anular 6561.

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

Fatorizar

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