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

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

Ovrednoti

$$-1187840000000000000000000$$

Koraki rešitve

Delite \frac{\left(125^{-2}\times 8^{-3}\right)^{-1}}{\left(25^{3}\times 16\right)^{-2}} s/z \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}} z obratno vrednostjo \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 potenco 125 števila -2, da dobite \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 potenco 8 števila -3, da dobite \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} in \frac{1}{512}, da dobite \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 potenco \frac{1}{8000000} števila -1, da dobite 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 in 25, da dobite 1600.

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

Izračunajte potenco 1600 števila 2, da dobite 2560000.

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

Pomnožite 8000000 in 2560000, da dobite 20480000000000.

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

Izračunajte potenco 25 števila 3, da dobite 15625.

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

Pomnožite 15625 in 16, da dobite 250000.

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

Izračunajte potenco 250000 števila -2, da dobite \frac{1}{62500000000}.

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

Izračunajte potenco 5 števila -3, da dobite \frac{1}{125}.

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

Izračunajte potenco 3 števila 2, da dobite 9.

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

Pomnožite \frac{1}{125} in 9, da dobite \frac{9}{125}.

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

Odštejte 1 od \frac{9}{125}, da dobite -\frac{116}{125}.

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

Izračunajte potenco -\frac{116}{125} števila -1, da dobite -\frac{125}{116}.

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

Pomnožite \frac{1}{62500000000} in -\frac{125}{116}, da dobite -\frac{1}{58000000000}.

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

Delite 20480000000000 s/z -\frac{1}{58000000000} tako, da pomnožite 20480000000000 z obratno vrednostjo -\frac{1}{58000000000}.

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

Pomnožite 20480000000000 in -58000000000, da dobite -1187840000000000000000000.

$$-1187840000000000000000000$$

Faktoriziraj

$$-1187840000000000000000000$$