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

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

Calcula

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

Passos de solució

Calculeu -27 elevat a 3 per obtenir -19683.

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

Calculeu 32 elevat a -2 per obtenir \frac{1}{1024}.

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

Multipliqueu -19683 per \frac{1}{1024} per obtenir -\frac{19683}{1024}.

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

Calculeu -8 elevat a 4 per obtenir 4096.

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

Multipliqueu -\frac{19683}{1024} per 4096 per obtenir -78732.

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

Calculeu 25 elevat a 2 per obtenir 625.

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

Multipliqueu -78732 per 625 per obtenir -49207500.

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

Calculeu -72 elevat a 4 per obtenir 26873856.

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

Calculeu 50 elevat a 3 per obtenir 125000.

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

Calculeu -125000 elevat a 4 per obtenir 244140625000000000000.

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

Multipliqueu 26873856 per 244140625000000000000 per obtenir 6561000000000000000000000000.

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

Redueix la fracció \frac{-49207500}{6561000000000000000000000000} al màxim extraient i anul·lant 16402500.

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

Factoritzar

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