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

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

Procijeni

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

Koraci za rješenje

Da biste podigli stepen na neki drugi stepen, 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 -27 stepen od 3 i dobijte -19683.

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

Izračunajte 32 stepen od -5 i dobijte \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 -8 stepen od 5 i dobijte -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 25 stepen od -12 i dobijte \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 -72 stepen od 4 i dobijte 26873856.

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

Izračunajte 50 stepen od 3 i dobijte 125000.

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

Izračunajte -125000 stepen od 4 i dobijte 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.

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

Svedite razlomak \frac{19683}{400451660156250000000000000000000000000000000000} na najprostije elemente rastavlјanjem i kraćenjem 6561.

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

Faktor

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