Atrisiniet (2*32^2-2/9*32^2-24*32+16:2*32-2/3*32-4-14*32/9*32^2-16)*(4+3*32)^2/32-1

$$( \frac { 2 \cdot 32 ^ { 2 } - 2 } { 9 \cdot 32 ^ { 2 } - 24 \cdot 32 + 16 } : \frac { 2 \cdot 32 - 2 } { 3 \cdot 32 - 4 } - \frac { 14 \cdot 32 } { 9 \cdot 32 ^ { 2 } - 16 } ) \cdot \frac { ( 4 + 3 \cdot 32 ) ^ { 2 } } { 32 - 1 }$$

Izrēķināt

$$100$$

Atrisinājuma darbības

Daliet \frac{2\times 32^{2}-2}{9\times 32^{2}-24\times 32+16} ar \frac{2\times 32-2}{3\times 32-4}, reizinot \frac{2\times 32^{2}-2}{9\times 32^{2}-24\times 32+16} ar apgriezto daļskaitli \frac{2\times 32-2}{3\times 32-4} .

$$\left(\frac{\left(2\times 32^{2}-2\right)\left(3\times 32-4\right)}{\left(9\times 32^{2}-24\times 32+16\right)\left(2\times 32-2\right)}-\frac{14\times 32}{9\times 32^{2}-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Aprēķiniet 32 pakāpē 2 un iegūstiet 1024.

$$\left(\frac{\left(2\times 1024-2\right)\left(3\times 32-4\right)}{\left(9\times 32^{2}-24\times 32+16\right)\left(2\times 32-2\right)}-\frac{14\times 32}{9\times 32^{2}-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Reiziniet 2 un 1024, lai iegūtu 2048.

$$\left(\frac{\left(2048-2\right)\left(3\times 32-4\right)}{\left(9\times 32^{2}-24\times 32+16\right)\left(2\times 32-2\right)}-\frac{14\times 32}{9\times 32^{2}-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Atņemiet 2 no 2048, lai iegūtu 2046.

$$\left(\frac{2046\left(3\times 32-4\right)}{\left(9\times 32^{2}-24\times 32+16\right)\left(2\times 32-2\right)}-\frac{14\times 32}{9\times 32^{2}-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Reiziniet 3 un 32, lai iegūtu 96.

$$\left(\frac{2046\left(96-4\right)}{\left(9\times 32^{2}-24\times 32+16\right)\left(2\times 32-2\right)}-\frac{14\times 32}{9\times 32^{2}-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Atņemiet 4 no 96, lai iegūtu 92.

$$\left(\frac{2046\times 92}{\left(9\times 32^{2}-24\times 32+16\right)\left(2\times 32-2\right)}-\frac{14\times 32}{9\times 32^{2}-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Reiziniet 2046 un 92, lai iegūtu 188232.

$$\left(\frac{188232}{\left(9\times 32^{2}-24\times 32+16\right)\left(2\times 32-2\right)}-\frac{14\times 32}{9\times 32^{2}-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Aprēķiniet 32 pakāpē 2 un iegūstiet 1024.

$$\left(\frac{188232}{\left(9\times 1024-24\times 32+16\right)\left(2\times 32-2\right)}-\frac{14\times 32}{9\times 32^{2}-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Reiziniet 9 un 1024, lai iegūtu 9216.

$$\left(\frac{188232}{\left(9216-24\times 32+16\right)\left(2\times 32-2\right)}-\frac{14\times 32}{9\times 32^{2}-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Reiziniet 24 un 32, lai iegūtu 768.

$$\left(\frac{188232}{\left(9216-768+16\right)\left(2\times 32-2\right)}-\frac{14\times 32}{9\times 32^{2}-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Atņemiet 768 no 9216, lai iegūtu 8448.

$$\left(\frac{188232}{\left(8448+16\right)\left(2\times 32-2\right)}-\frac{14\times 32}{9\times 32^{2}-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Saskaitiet 8448 un 16, lai iegūtu 8464.

$$\left(\frac{188232}{8464\left(2\times 32-2\right)}-\frac{14\times 32}{9\times 32^{2}-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Reiziniet 2 un 32, lai iegūtu 64.

$$\left(\frac{188232}{8464\left(64-2\right)}-\frac{14\times 32}{9\times 32^{2}-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Atņemiet 2 no 64, lai iegūtu 62.

$$\left(\frac{188232}{8464\times 62}-\frac{14\times 32}{9\times 32^{2}-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Reiziniet 8464 un 62, lai iegūtu 524768.

$$\left(\frac{188232}{524768}-\frac{14\times 32}{9\times 32^{2}-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Vienādot daļskaitli \frac{188232}{524768} līdz mazākajam loceklim, izvelkot un saīsinot 5704.

$$\left(\frac{33}{92}-\frac{14\times 32}{9\times 32^{2}-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Reiziniet 14 un 32, lai iegūtu 448.

$$\left(\frac{33}{92}-\frac{448}{9\times 32^{2}-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Aprēķiniet 32 pakāpē 2 un iegūstiet 1024.

$$\left(\frac{33}{92}-\frac{448}{9\times 1024-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Reiziniet 9 un 1024, lai iegūtu 9216.

$$\left(\frac{33}{92}-\frac{448}{9216-16}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Atņemiet 16 no 9216, lai iegūtu 9200.

$$\left(\frac{33}{92}-\frac{448}{9200}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Vienādot daļskaitli \frac{448}{9200} līdz mazākajam loceklim, izvelkot un saīsinot 16.

$$\left(\frac{33}{92}-\frac{28}{575}\right)\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Atņemiet \frac{28}{575} no \frac{33}{92}, lai iegūtu \frac{31}{100}.

$$\frac{31}{100}\times \frac{\left(4+3\times 32\right)^{2}}{32-1}$$

Reiziniet 3 un 32, lai iegūtu 96.

$$\frac{31}{100}\times \frac{\left(4+96\right)^{2}}{32-1}$$

Saskaitiet 4 un 96, lai iegūtu 100.

$$\frac{31}{100}\times \frac{100^{2}}{32-1}$$

Aprēķiniet 100 pakāpē 2 un iegūstiet 10000.

$$\frac{31}{100}\times \frac{10000}{32-1}$$

Atņemiet 1 no 32, lai iegūtu 31.

$$\frac{31}{100}\times \frac{10000}{31}$$

Reiziniet \frac{31}{100} un \frac{10000}{31}, lai iegūtu 100.

$$100$$

Sadalīt reizinātājos

$$2^{2}\times 5^{2}$$