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

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

Izračunaj

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

Koraci rješenja

Da biste izračunali potenciju potencije, pomnožite eksponente. Pomnožite 2 i -6 da biste dobili -12.

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

Izračunajte koliko je 3 na -27 da biste dobili -19683.

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

Izračunajte koliko je -5 na 32 da biste dobili \frac{1}{33554432}.

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

Pomnožite -19683 i \frac{1}{33554432} da biste dobili -\frac{19683}{33554432}.

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

Izračunajte koliko je 5 na -8 da biste dobili -32768.

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

Pomnožite -\frac{19683}{33554432} i -32768 da biste dobili \frac{19683}{1024}.

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

Izračunajte koliko je -12 na 25 da biste dobili \frac{1}{59604644775390625}.

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

Pomnožite \frac{19683}{1024} i \frac{1}{59604644775390625} da biste dobili \frac{19683}{61035156250000000000}.

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

Izračunajte koliko je 4 na -72 da biste dobili 26873856.

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

Izračunajte koliko je 3 na 50 da biste dobili 125000.

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

Izračunajte koliko je 4 na -125000 da biste dobili 244140625000000000000.

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

Pomnožite 26873856 i 244140625000000000000 da biste dobili 6561000000000000000000000000.

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

Izrazite \frac{\frac{19683}{61035156250000000000}}{6561000000000000000000000000} kao jedan razlomak.

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

Pomnožite 61035156250000000000 i 6561000000000000000000000000 da biste dobili 400451660156250000000000000000000000000000000000.

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

Skratite razlomak \frac{19683}{400451660156250000000000000000000000000000000000} na najmanje vrijednosti tako da izlučite i poništite 6561.

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

Faktor

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