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

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

Izrēķināt

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

Atrisinājuma darbības

Lai pakāpi kāpinātu citā pakāpē, sareiziniet kāpinātājus. Sareiziniet 2 un -6, lai iegūtu -12.

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

Aprēķiniet -27 pakāpē 3 un iegūstiet -19683.

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

Aprēķiniet 32 pakāpē -5 un iegūstiet \frac{1}{33554432}.

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

Reiziniet -19683 un \frac{1}{33554432}, lai iegūtu -\frac{19683}{33554432}.

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

Aprēķiniet -8 pakāpē 5 un iegūstiet -32768.

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

Reiziniet -\frac{19683}{33554432} un -32768, lai iegūtu \frac{19683}{1024}.

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

Aprēķiniet 25 pakāpē -12 un iegūstiet \frac{1}{59604644775390625}.

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

Reiziniet \frac{19683}{1024} un \frac{1}{59604644775390625}, lai iegūtu \frac{19683}{61035156250000000000}.

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

Aprēķiniet -72 pakāpē 4 un iegūstiet 26873856.

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

Aprēķiniet 50 pakāpē 3 un iegūstiet 125000.

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

Aprēķiniet -125000 pakāpē 4 un iegūstiet 244140625000000000000.

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

Reiziniet 26873856 un 244140625000000000000, lai iegūtu 6561000000000000000000000000.

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

Izsakiet \frac{\frac{19683}{61035156250000000000}}{6561000000000000000000000000} kā vienu daļskaitli.

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

Reiziniet 61035156250000000000 un 6561000000000000000000000000, lai iegūtu 400451660156250000000000000000000000000000000000.

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

Vienādot daļskaitli \frac{19683}{400451660156250000000000000000000000000000000000} līdz mazākajam loceklim, izvelkot un saīsinot 6561.

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

Sadalīt reizinātājos

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