Solve (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

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

Evaluate

$$100$$

Solution Steps

Divide \frac{2\times 32^{2}-2}{9\times 32^{2}-24\times 32+16} by \frac{2\times 32-2}{3\times 32-4} by multiplying \frac{2\times 32^{2}-2}{9\times 32^{2}-24\times 32+16} by the reciprocal of \frac{2\times 32-2}{3\times 32-4}.

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

Calculate 32 to the power of 2 and get 1024.

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

Multiply 2 and 1024 to get 2048.

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

Subtract 2 from 2048 to get 2046.

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

Multiply 3 and 32 to get 96.

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

Subtract 4 from 96 to get 92.

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

Multiply 2046 and 92 to get 188232.

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

Calculate 32 to the power of 2 and get 1024.

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

Multiply 9 and 1024 to get 9216.

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

Multiply 24 and 32 to get 768.

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

Subtract 768 from 9216 to get 8448.

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

Add 8448 and 16 to get 8464.

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

Multiply 2 and 32 to get 64.

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

Subtract 2 from 64 to get 62.

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

Multiply 8464 and 62 to get 524768.

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

Reduce the fraction \frac{188232}{524768} to lowest terms by extracting and canceling out 5704.

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

Multiply 14 and 32 to get 448.

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

Calculate 32 to the power of 2 and get 1024.

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

Multiply 9 and 1024 to get 9216.

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

Subtract 16 from 9216 to get 9200.

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

Reduce the fraction \frac{448}{9200} to lowest terms by extracting and canceling out 16.

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

Subtract \frac{28}{575} from \frac{33}{92} to get \frac{31}{100}.

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

Multiply 3 and 32 to get 96.

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

Add 4 and 96 to get 100.

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

Calculate 100 to the power of 2 and get 10000.

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

Subtract 1 from 32 to get 31.

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

Multiply \frac{31}{100} and \frac{10000}{31} to get 100.

$$100$$

Factor

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