Riješi (frac{-2(-2)^{2}*(1/9)^{3}}{(-15)^{4}})^{3}:((-15)^7/2(-2)^2*(frac{1{9})^4})^-2

$$( \frac { - 2 ( - 2 ) ^ { 2 } \cdot ( \frac { 1 } { 9 } ) ^ { 3 } } { ( - 15 ) ^ { 4 } } ) ^ { 3 } : ( \frac { ( - 15 ) ^ { 7 } } { 2 ( - 2 ) ^ { 2 } \cdot ( \frac { 1 } { 9 } ) ^ { 4 } } ) ^ { - 2 }$$

Izračunaj

$$-200$$

Koraci rješenja

Da biste pomnožili potencije s istom bazom, zbrojite eksponente. Dodajte 1 i 2 da biste dobili 3.

$$\frac{\left(\frac{\left(-2\right)^{3}\times \left(\frac{1}{9}\right)^{3}}{\left(-15\right)^{4}}\right)^{3}}{\left(\frac{\left(-15\right)^{7}}{2\left(-2\right)^{2}\times \left(\frac{1}{9}\right)^{4}}\right)^{-2}}$$

Izračunajte koliko je 3 na -2 da biste dobili -8.

$$\frac{\left(\frac{-8\times \left(\frac{1}{9}\right)^{3}}{\left(-15\right)^{4}}\right)^{3}}{\left(\frac{\left(-15\right)^{7}}{2\left(-2\right)^{2}\times \left(\frac{1}{9}\right)^{4}}\right)^{-2}}$$

Izračunajte koliko je 3 na \frac{1}{9} da biste dobili \frac{1}{729}.

$$\frac{\left(\frac{-8\times \frac{1}{729}}{\left(-15\right)^{4}}\right)^{3}}{\left(\frac{\left(-15\right)^{7}}{2\left(-2\right)^{2}\times \left(\frac{1}{9}\right)^{4}}\right)^{-2}}$$

Pomnožite -8 i \frac{1}{729} da biste dobili -\frac{8}{729}.

$$\frac{\left(\frac{-\frac{8}{729}}{\left(-15\right)^{4}}\right)^{3}}{\left(\frac{\left(-15\right)^{7}}{2\left(-2\right)^{2}\times \left(\frac{1}{9}\right)^{4}}\right)^{-2}}$$

Izračunajte koliko je 4 na -15 da biste dobili 50625.

$$\frac{\left(\frac{-\frac{8}{729}}{50625}\right)^{3}}{\left(\frac{\left(-15\right)^{7}}{2\left(-2\right)^{2}\times \left(\frac{1}{9}\right)^{4}}\right)^{-2}}$$

Izrazite \frac{-\frac{8}{729}}{50625} kao jedan razlomak.

$$\frac{\left(\frac{-8}{729\times 50625}\right)^{3}}{\left(\frac{\left(-15\right)^{7}}{2\left(-2\right)^{2}\times \left(\frac{1}{9}\right)^{4}}\right)^{-2}}$$

Pomnožite 729 i 50625 da biste dobili 36905625.

$$\frac{\left(\frac{-8}{36905625}\right)^{3}}{\left(\frac{\left(-15\right)^{7}}{2\left(-2\right)^{2}\times \left(\frac{1}{9}\right)^{4}}\right)^{-2}}$$

Razlomak \frac{-8}{36905625} može se napisati kao -\frac{8}{36905625} tako da se izluči negativan predznak.

$$\frac{\left(-\frac{8}{36905625}\right)^{3}}{\left(\frac{\left(-15\right)^{7}}{2\left(-2\right)^{2}\times \left(\frac{1}{9}\right)^{4}}\right)^{-2}}$$

Izračunajte koliko je 3 na -\frac{8}{36905625} da biste dobili -\frac{512}{50266389671545166015625}.

$$\frac{-\frac{512}{50266389671545166015625}}{\left(\frac{\left(-15\right)^{7}}{2\left(-2\right)^{2}\times \left(\frac{1}{9}\right)^{4}}\right)^{-2}}$$

Izračunajte koliko je 7 na -15 da biste dobili -170859375.

$$\frac{-\frac{512}{50266389671545166015625}}{\left(\frac{-170859375}{2\left(-2\right)^{2}\times \left(\frac{1}{9}\right)^{4}}\right)^{-2}}$$

Izračunajte koliko je 2 na -2 da biste dobili 4.

$$\frac{-\frac{512}{50266389671545166015625}}{\left(\frac{-170859375}{2\times 4\times \left(\frac{1}{9}\right)^{4}}\right)^{-2}}$$

Pomnožite 2 i 4 da biste dobili 8.

$$\frac{-\frac{512}{50266389671545166015625}}{\left(\frac{-170859375}{8\times \left(\frac{1}{9}\right)^{4}}\right)^{-2}}$$

Izračunajte koliko je 4 na \frac{1}{9} da biste dobili \frac{1}{6561}.

$$\frac{-\frac{512}{50266389671545166015625}}{\left(\frac{-170859375}{8\times \frac{1}{6561}}\right)^{-2}}$$

Pomnožite 8 i \frac{1}{6561} da biste dobili \frac{8}{6561}.

$$\frac{-\frac{512}{50266389671545166015625}}{\left(\frac{-170859375}{\frac{8}{6561}}\right)^{-2}}$$

Podijelite -170859375 s \frac{8}{6561} tako da pomnožite -170859375 s brojem recipročnim broju \frac{8}{6561}.

$$\frac{-\frac{512}{50266389671545166015625}}{\left(-170859375\times \frac{6561}{8}\right)^{-2}}$$

Pomnožite -170859375 i \frac{6561}{8} da biste dobili -\frac{1121008359375}{8}.

$$\frac{-\frac{512}{50266389671545166015625}}{\left(-\frac{1121008359375}{8}\right)^{-2}}$$

Izračunajte koliko je -2 na -\frac{1121008359375}{8} da biste dobili \frac{64}{1256659741788629150390625}.

$$\frac{-\frac{512}{50266389671545166015625}}{\frac{64}{1256659741788629150390625}}$$

Podijelite -\frac{512}{50266389671545166015625} s \frac{64}{1256659741788629150390625} tako da pomnožite -\frac{512}{50266389671545166015625} s brojem recipročnim broju \frac{64}{1256659741788629150390625}.

$$-\frac{512}{50266389671545166015625}\times \frac{1256659741788629150390625}{64}$$

Pomnožite -\frac{512}{50266389671545166015625} i \frac{1256659741788629150390625}{64} da biste dobili -200.

$$-200$$

Faktor

$$-200$$