Solve 2160^340/12+2*144*440^2+40^380/12+48^22*{40}^2

$$2 \frac{ { 160 }^{ 3 } 40 }{ 12 } +2 \cdot 144 \cdot 4 { 40 }^{ 2 } + \frac{ { 40 }^{ 3 } 80 }{ 12 } + { 48 }^{ 2 } 2 \times { 40 }^{ 2 }$$

Evaluate

$$\frac{110848000}{3}\approx 36949333.333333333$$

Solution Steps

Calculate 160 to the power of 3 and get 4096000.

$$2\times \frac{4096000\times 40}{12}+2\times 144\times 4\times 40^{2}+\frac{40^{3}\times 80}{12}+48^{2}\times 2\times 40^{2}$$

Multiply 4096000 and 40 to get 163840000.

$$2\times \frac{163840000}{12}+2\times 144\times 4\times 40^{2}+\frac{40^{3}\times 80}{12}+48^{2}\times 2\times 40^{2}$$

Reduce the fraction \frac{163840000}{12} to lowest terms by extracting and canceling out 4.

$$2\times \frac{40960000}{3}+2\times 144\times 4\times 40^{2}+\frac{40^{3}\times 80}{12}+48^{2}\times 2\times 40^{2}$$

Express 2\times \frac{40960000}{3} as a single fraction.

$$\frac{2\times 40960000}{3}+2\times 144\times 4\times 40^{2}+\frac{40^{3}\times 80}{12}+48^{2}\times 2\times 40^{2}$$

Multiply 2 and 40960000 to get 81920000.

$$\frac{81920000}{3}+2\times 144\times 4\times 40^{2}+\frac{40^{3}\times 80}{12}+48^{2}\times 2\times 40^{2}$$

Multiply 2 and 144 to get 288.

$$\frac{81920000}{3}+288\times 4\times 40^{2}+\frac{40^{3}\times 80}{12}+48^{2}\times 2\times 40^{2}$$

Multiply 288 and 4 to get 1152.

$$\frac{81920000}{3}+1152\times 40^{2}+\frac{40^{3}\times 80}{12}+48^{2}\times 2\times 40^{2}$$

Calculate 40 to the power of 2 and get 1600.

$$\frac{81920000}{3}+1152\times 1600+\frac{40^{3}\times 80}{12}+48^{2}\times 2\times 40^{2}$$

Multiply 1152 and 1600 to get 1843200.

$$\frac{81920000}{3}+1843200+\frac{40^{3}\times 80}{12}+48^{2}\times 2\times 40^{2}$$

Convert 1843200 to fraction \frac{5529600}{3}.

$$\frac{81920000}{3}+\frac{5529600}{3}+\frac{40^{3}\times 80}{12}+48^{2}\times 2\times 40^{2}$$

Since \frac{81920000}{3} and \frac{5529600}{3} have the same denominator, add them by adding their numerators.

$$\frac{81920000+5529600}{3}+\frac{40^{3}\times 80}{12}+48^{2}\times 2\times 40^{2}$$

Add 81920000 and 5529600 to get 87449600.

$$\frac{87449600}{3}+\frac{40^{3}\times 80}{12}+48^{2}\times 2\times 40^{2}$$

Calculate 40 to the power of 3 and get 64000.

$$\frac{87449600}{3}+\frac{64000\times 80}{12}+48^{2}\times 2\times 40^{2}$$

Multiply 64000 and 80 to get 5120000.

$$\frac{87449600}{3}+\frac{5120000}{12}+48^{2}\times 2\times 40^{2}$$

Reduce the fraction \frac{5120000}{12} to lowest terms by extracting and canceling out 4.

$$\frac{87449600}{3}+\frac{1280000}{3}+48^{2}\times 2\times 40^{2}$$

Since \frac{87449600}{3} and \frac{1280000}{3} have the same denominator, add them by adding their numerators.

$$\frac{87449600+1280000}{3}+48^{2}\times 2\times 40^{2}$$

Add 87449600 and 1280000 to get 88729600.

$$\frac{88729600}{3}+48^{2}\times 2\times 40^{2}$$

Calculate 48 to the power of 2 and get 2304.

$$\frac{88729600}{3}+2304\times 2\times 40^{2}$$

Multiply 2304 and 2 to get 4608.

$$\frac{88729600}{3}+4608\times 40^{2}$$

Calculate 40 to the power of 2 and get 1600.

$$\frac{88729600}{3}+4608\times 1600$$

Multiply 4608 and 1600 to get 7372800.

$$\frac{88729600}{3}+7372800$$

Convert 7372800 to fraction \frac{22118400}{3}.

$$\frac{88729600}{3}+\frac{22118400}{3}$$

Since \frac{88729600}{3} and \frac{22118400}{3} have the same denominator, add them by adding their numerators.

$$\frac{88729600+22118400}{3}$$

Add 88729600 and 22118400 to get 110848000.

$$\frac{110848000}{3}$$

Factor

$$\frac{2 ^ {11} \cdot 5 ^ {3} \cdot 433}{3} = 36949333\frac{1}{3} = 36949333.333333336$$