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

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

Izrēķināt

$$-1187840000000000000000000$$

Atrisinājuma darbības

Daliet \frac{\left(125^{-2}\times 8^{-3}\right)^{-1}}{\left(25^{3}\times 16\right)^{-2}} ar \frac{\left(5^{-3}\times 3^{2}-1\right)^{-1}}{\left(64\times 25\right)^{2}}, reizinot \frac{\left(125^{-2}\times 8^{-3}\right)^{-1}}{\left(25^{3}\times 16\right)^{-2}} ar apgriezto daļskaitli \frac{\left(5^{-3}\times 3^{2}-1\right)^{-1}}{\left(64\times 25\right)^{2}} .

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

Aprēķiniet 125 pakāpē -2 un iegūstiet \frac{1}{15625}.

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

Aprēķiniet 8 pakāpē -3 un iegūstiet \frac{1}{512}.

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

Reiziniet \frac{1}{15625} un \frac{1}{512}, lai iegūtu \frac{1}{8000000}.

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

Aprēķiniet \frac{1}{8000000} pakāpē -1 un iegūstiet 8000000.

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

Reiziniet 64 un 25, lai iegūtu 1600.

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

Aprēķiniet 1600 pakāpē 2 un iegūstiet 2560000.

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

Reiziniet 8000000 un 2560000, lai iegūtu 20480000000000.

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

Aprēķiniet 25 pakāpē 3 un iegūstiet 15625.

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

Reiziniet 15625 un 16, lai iegūtu 250000.

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

Aprēķiniet 250000 pakāpē -2 un iegūstiet \frac{1}{62500000000}.

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

Aprēķiniet 5 pakāpē -3 un iegūstiet \frac{1}{125}.

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

Aprēķiniet 3 pakāpē 2 un iegūstiet 9.

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

Reiziniet \frac{1}{125} un 9, lai iegūtu \frac{9}{125}.

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

Atņemiet 1 no \frac{9}{125}, lai iegūtu -\frac{116}{125}.

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

Aprēķiniet -\frac{116}{125} pakāpē -1 un iegūstiet -\frac{125}{116}.

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

Reiziniet \frac{1}{62500000000} un -\frac{125}{116}, lai iegūtu -\frac{1}{58000000000}.

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

Daliet 20480000000000 ar -\frac{1}{58000000000}, reizinot 20480000000000 ar apgriezto daļskaitli -\frac{1}{58000000000} .

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

Reiziniet 20480000000000 un -58000000000, lai iegūtu -1187840000000000000000000.

$$-1187840000000000000000000$$

Sadalīt reizinātājos

$$-1187840000000000000000000$$