Riješi frac{[(125)^{-2}*8^{-3}]^{-1}}{[25^{3}*16]^{-2}}div[5^-3*3^2-1]^-1/[64*25]^2

$$\frac { [ ( 125 ) ^ { - 2 } \cdot 8 ^ { - 3 } ] ^ { - 1 } } { [ 25 ^ { 3 } \cdot 16 ] ^ { - 2 } } \div \frac { [ 5 ^ { - 3 } \cdot 3 ^ { 2 } - 1 ] ^ { - 1 } } { [ 64 \cdot 25 ] ^ { 2 } }$$

Izračunaj

$$-1187840000000000000000000$$

Koraci rješenja

Podijelite \frac{\left(125^{-2}\times 8^{-3}\right)^{-1}}{\left(25^{3}\times 16\right)^{-2}} s \frac{\left(5^{-3}\times 3^{2}-1\right)^{-1}}{\left(64\times 25\right)^{2}} tako da pomnožite \frac{\left(125^{-2}\times 8^{-3}\right)^{-1}}{\left(25^{3}\times 16\right)^{-2}} s brojem recipročnim broju \frac{\left(5^{-3}\times 3^{2}-1\right)^{-1}}{\left(64\times 25\right)^{2}}.

$$\frac{\left(125^{-2}\times 8^{-3}\right)^{-1}\times \left(64\times 25\right)^{2}}{\left(25^{3}\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Izračunajte koliko je -2 na 125 da biste dobili \frac{1}{15625}.

$$\frac{\left(\frac{1}{15625}\times 8^{-3}\right)^{-1}\times \left(64\times 25\right)^{2}}{\left(25^{3}\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Izračunajte koliko je -3 na 8 da biste dobili \frac{1}{512}.

$$\frac{\left(\frac{1}{15625}\times \frac{1}{512}\right)^{-1}\times \left(64\times 25\right)^{2}}{\left(25^{3}\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Pomnožite \frac{1}{15625} i \frac{1}{512} da biste dobili \frac{1}{8000000}.

$$\frac{\left(\frac{1}{8000000}\right)^{-1}\times \left(64\times 25\right)^{2}}{\left(25^{3}\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Izračunajte koliko je -1 na \frac{1}{8000000} da biste dobili 8000000.

$$\frac{8000000\times \left(64\times 25\right)^{2}}{\left(25^{3}\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Pomnožite 64 i 25 da biste dobili 1600.

$$\frac{8000000\times 1600^{2}}{\left(25^{3}\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Izračunajte koliko je 2 na 1600 da biste dobili 2560000.

$$\frac{8000000\times 2560000}{\left(25^{3}\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Pomnožite 8000000 i 2560000 da biste dobili 20480000000000.

$$\frac{20480000000000}{\left(25^{3}\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Izračunajte koliko je 3 na 25 da biste dobili 15625.

$$\frac{20480000000000}{\left(15625\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Pomnožite 15625 i 16 da biste dobili 250000.

$$\frac{20480000000000}{250000^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Izračunajte koliko je -2 na 250000 da biste dobili \frac{1}{62500000000}.

$$\frac{20480000000000}{\frac{1}{62500000000}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Izračunajte koliko je -3 na 5 da biste dobili \frac{1}{125}.

$$\frac{20480000000000}{\frac{1}{62500000000}\left(\frac{1}{125}\times 3^{2}-1\right)^{-1}}$$

Izračunajte koliko je 2 na 3 da biste dobili 9.

$$\frac{20480000000000}{\frac{1}{62500000000}\left(\frac{1}{125}\times 9-1\right)^{-1}}$$

Pomnožite \frac{1}{125} i 9 da biste dobili \frac{9}{125}.

$$\frac{20480000000000}{\frac{1}{62500000000}\left(\frac{9}{125}-1\right)^{-1}}$$

Oduzmite 1 od \frac{9}{125} da biste dobili -\frac{116}{125}.

$$\frac{20480000000000}{\frac{1}{62500000000}\left(-\frac{116}{125}\right)^{-1}}$$

Izračunajte koliko je -1 na -\frac{116}{125} da biste dobili -\frac{125}{116}.

$$\frac{20480000000000}{\frac{1}{62500000000}\left(-\frac{125}{116}\right)}$$

Pomnožite \frac{1}{62500000000} i -\frac{125}{116} da biste dobili -\frac{1}{58000000000}.

$$\frac{20480000000000}{-\frac{1}{58000000000}}$$

Podijelite 20480000000000 s -\frac{1}{58000000000} tako da pomnožite 20480000000000 s brojem recipročnim broju -\frac{1}{58000000000}.

$$20480000000000\left(-58000000000\right)$$

Pomnožite 20480000000000 i -58000000000 da biste dobili -1187840000000000000000000.

$$-1187840000000000000000000$$

Faktor

$$-1187840000000000000000000$$