Solve 200*10^3/12+2000*277^2+10*380^3/123800*82^2+frac{200{10}^{3}}{12}2000*{113}^2+frac{250*{20}^3}{{12}^1}+5000*{128}^2

$$\frac{ 200 \times { 10 }^{ 3 } }{ 12 } +2000 \times { 277 }^{ 2 } + \frac{ 10 \times { 380 }^{ 3 } }{ 12 } 3800 \times { 82 }^{ 2 } + \frac{ 200 { 10 }^{ 3 } }{ 12 } 2000 \times { 113 }^{ 2 } + \frac{ 250 \times { 20 }^{ 3 } }{ { 12 }^{ 1 } } +5000 \times { 128 }^{ 2 }$$

Evaluate

$$1168797074228000$$

Solution Steps

Calculate 10 to the power of 3 and get 1000.

$$\frac{200\times 1000}{12}+2000\times 277^{2}+\frac{10\times 380^{3}}{12}\times 3800\times 82^{2}+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Multiply 200 and 1000 to get 200000.

$$\frac{200000}{12}+2000\times 277^{2}+\frac{10\times 380^{3}}{12}\times 3800\times 82^{2}+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Reduce the fraction \frac{200000}{12} to lowest terms by extracting and canceling out 4.

$$\frac{50000}{3}+2000\times 277^{2}+\frac{10\times 380^{3}}{12}\times 3800\times 82^{2}+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Calculate 277 to the power of 2 and get 76729.

$$\frac{50000}{3}+2000\times 76729+\frac{10\times 380^{3}}{12}\times 3800\times 82^{2}+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Multiply 2000 and 76729 to get 153458000.

$$\frac{50000}{3}[phone]+\frac{10\times 380^{3}}{12}\times 3800\times 82^{2}+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Convert 153458000 to fraction \frac{460374000}{3}.

$$\frac{50000}{3}+\frac{460374000}{3}+\frac{10\times 380^{3}}{12}\times 3800\times 82^{2}+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Since \frac{50000}{3} and \frac{460374000}{3} have the same denominator, add them by adding their numerators.

$$\frac{50000+460374000}{3}+\frac{10\times 380^{3}}{12}\times 3800\times 82^{2}+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Add 50000 and 460374000 to get 460424000.

$$\frac{460424000}{3}+\frac{10\times 380^{3}}{12}\times 3800\times 82^{2}+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Calculate 380 to the power of 3 and get 54872000.

$$\frac{460424000}{3}+\frac{10\times 54872000}{12}\times 3800\times 82^{2}+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Multiply 10 and 54872000 to get 548720000.

$$\frac{460424000}{3}+\frac{548720000}{12}\times 3800\times 82^{2}+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Reduce the fraction \frac{548720000}{12} to lowest terms by extracting and canceling out 4.

$$\frac{460424000}{3}+\frac{137180000}{3}\times 3800\times 82^{2}+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Express \frac{137180000}{3}\times 3800 as a single fraction.

$$\frac{460424000}{3}+\frac{137180000\times 3800}{3}\times 82^{2}+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Multiply 137180000 and 3800 to get 521284000000.

$$\frac{460424000}{3}+\frac{521284000000}{3}\times 82^{2}+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Calculate 82 to the power of 2 and get 6724.

$$\frac{460424000}{3}+\frac{521284000000}{3}\times 6724+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Express \frac{521284000000}{3}\times 6724 as a single fraction.

$$\frac{460424000}{3}+\frac{521284000000\times 6724}{3}+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Multiply 521284000000 and 6724 to get 3505113616000000.

$$\frac{460424000}{3}+\frac{3505113616000000}{3}+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Since \frac{460424000}{3} and \frac{3505113616000000}{3} have the same denominator, add them by adding their numerators.

$$\frac{460424000+3505113616000000}{3}+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Add 460424000 and 3505113616000000 to get 3505114076424000.

$$\frac{3505114076424000}{3}+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Divide 3505114076424000 by 3 to get 1168371358808000.

$$1168371358808000+\frac{200\times 10^{3}}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Calculate 10 to the power of 3 and get 1000.

$$1168371358808000+\frac{200\times 1000}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Multiply 200 and 1000 to get 200000.

$$1168371358808000+\frac{200000}{12}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Reduce the fraction \frac{200000}{12} to lowest terms by extracting and canceling out 4.

$$1168371358808000+\frac{50000}{3}\times 2000\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Express \frac{50000}{3}\times 2000 as a single fraction.

$$1168371358808000+\frac{50000\times 2000}{3}\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Multiply 50000 and 2000 to get 100000000.

$$1168371358808000+\frac{100000000}{3}\times 113^{2}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Calculate 113 to the power of 2 and get 12769.

$$1168371358808000+\frac{100000000}{3}\times 12769+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Express \frac{100000000}{3}\times 12769 as a single fraction.

$$1168371358808000+\frac{100000000\times 12769}{3}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Multiply 100000000 and 12769 to get 1276900000000.

$$1168371358808000+\frac{1276900000000}{3}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Convert 1168371358808000 to fraction \frac{3505114076424000}{3}.

$$\frac{3505114076424000}{3}+\frac{1276900000000}{3}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Since \frac{3505114076424000}{3} and \frac{1276900000000}{3} have the same denominator, add them by adding their numerators.

$$\frac{3505114076424000+1276900000000}{3}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Add 3505114076424000 and 1276900000000 to get 3506390976424000.

$$\frac{3506390976424000}{3}+\frac{250\times 20^{3}}{12^{1}}+5000\times 128^{2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3506390976424000}{3}+\frac{125\times 20^{3}}{6}+5000\times 128^{2}$$

Calculate 20 to the power of 3 and get 8000.

$$\frac{3506390976424000}{3}+\frac{125\times 8000}{6}+5000\times 128^{2}$$

Multiply 125 and 8000 to get 1000000.

$$\frac{3506390976424000}{3}+\frac{1000000}{6}+5000\times 128^{2}$$

Reduce the fraction \frac{1000000}{6} to lowest terms by extracting and canceling out 2.

$$\frac{3506390976424000}{3}+\frac{500000}{3}+5000\times 128^{2}$$

Since \frac{3506390976424000}{3} and \frac{500000}{3} have the same denominator, add them by adding their numerators.

$$\frac{3506390976424000+500000}{3}+5000\times 128^{2}$$

Add 3506390976424000 and 500000 to get 3506390976924000.

$$\frac{3506390976924000}{3}+5000\times 128^{2}$$

Divide 3506390976924000 by 3 to get 1168796992308000.

$$1168796992308000+5000\times 128^{2}$$

Calculate 128 to the power of 2 and get 16384.

$$1168796992308000+5000\times 16384$$

Multiply 5000 and 16384 to get 81920000.

$$1168796992308000+81920000$$

Add 1168796992308000 and 81920000 to get 1168797074228000.

$$1168797074228000$$

Factor

$$2^{5}\times 5^{3}\times 7\times 313\times 5927\times 22501$$