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

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

Avaliar

$$-\frac{3}{400000000000000000000}=-7,5 \cdot 10^{-21}$$

Passos Para a Resolução

Calcule -27 elevado a 3 e obtenha -19683.

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

Calcule 32 elevado a -2 e obtenha \frac{1}{1024}.

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

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

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

Calcule -8 elevado a 4 e obtenha 4096.

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

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

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

Calcule 25 elevado a 2 e obtenha 625.

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

Multiplique -78732 e 625 para obter -49207500.

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

Calcule -72 elevado a 4 e obtenha 26873856.

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

Calcule 50 elevado a 3 e obtenha 125000.

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

Calcule -125000 elevado a 4 e obtenha 244140625000000000000.

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

Multiplique 26873856 e 244140625000000000000 para obter 6561000000000000000000000000.

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

Reduza a fração \frac{-49207500}{6561000000000000000000000000} para os termos mais baixos ao retirar e anular 16402500.

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

Fatorizar

$$-\frac{3}{400000000000000000000} = -7,500000000000002 \times 10^{-21}$$