Solve 400left(6*306-74*14right)^2/left(6+14right)left(74+306right)(6+306)*(14+306)

$$\frac{ 400 { \left(6 \cdot 306-74 \cdot 14 \right) }^{ 2 } }{ \left( 6+14 \right) \left( 74+306 \right) (6+306) \cdot (14+306) }$$

Evaluate

$$\frac{250}{741}\approx 0.337381916$$

Solution Steps

Multiply 6 and 306 to get 1836.

$$\frac{400\left(1836-74\times 14\right)^{2}}{\left(6+14\right)\left(74+306\right)\left(6+306\right)\left(14+306\right)}$$

Multiply 74 and 14 to get 1036.

$$\frac{400\left(1836-1036\right)^{2}}{\left(6+14\right)\left(74+306\right)\left(6+306\right)\left(14+306\right)}$$

Subtract 1036 from 1836 to get 800.

$$\frac{400\times 800^{2}}{\left(6+14\right)\left(74+306\right)\left(6+306\right)\left(14+306\right)}$$

Calculate 800 to the power of 2 and get 640000.

$$\frac{400\times 640000}{\left(6+14\right)\left(74+306\right)\left(6+306\right)\left(14+306\right)}$$

Multiply 400 and 640000 to get 256000000.

$$\frac{256000000}{\left(6+14\right)\left(74+306\right)\left(6+306\right)\left(14+306\right)}$$

Add 6 and 14 to get 20.

$$\frac{256000000}{20\left(74+306\right)\left(6+306\right)\left(14+306\right)}$$

Add 74 and 306 to get 380.

$$\frac{256000000}{20\times 380\left(6+306\right)\left(14+306\right)}$$

Multiply 20 and 380 to get 7600.

$$\frac{256000000}{7600\left(6+306\right)\left(14+306\right)}$$

Add 6 and 306 to get 312.

$$\frac{256000000}{7600\times 312\left(14+306\right)}$$

Multiply 7600 and 312 to get 2371200.

$$\frac{256000000}{2371200\left(14+306\right)}$$

Add 14 and 306 to get 320.

$$\frac{256000000}{2371200\times 320}$$

Multiply 2371200 and 320 to get 758784000.

$$\frac{256000000}{758784000}$$

Reduce the fraction \frac{256000000}{758784000} to lowest terms by extracting and canceling out 1024000.

$$\frac{250}{741}$$

Factor

$$\frac{2 \cdot 5 ^ {3}}{3 \cdot 13 \cdot 19} = 0.33738191632928477$$