Solve left(580*470-530*420right)^2*2000div1000div1000div1110div990=

$${ \left(580 \times 470-530 \times 420 \right) }^{ 2 } \times 2000 \div 1000 \div 1000 \div 1110 \div 990=$$

Evaluate

$$\frac{50000}{10989}\approx 4.55000455$$

Solution Steps

Express \frac{\frac{\frac{\frac{\left(580\times 470-530\times 420\right)^{2}\times 2000}{1000}}{1000}}{1110}}{990} as a single fraction.

$$\frac{\frac{\frac{\left(580\times 470-530\times 420\right)^{2}\times 2000}{1000}}{1000}}{1110\times 990}$$

Express \frac{\frac{\left(580\times 470-530\times 420\right)^{2}\times 2000}{1000}}{1000} as a single fraction.

$$\frac{\frac{\left(580\times 470-530\times 420\right)^{2}\times 2000}{1000\times 1000}}{1110\times 990}$$

Cancel out 2\times 1000 in both numerator and denominator.

$$\frac{\frac{\left(470\times 580-420\times 530\right)^{2}}{500}}{1110\times 990}$$

Multiply 470 and 580 to get 272600.

$$\frac{\frac{\left(272600-420\times 530\right)^{2}}{500}}{1110\times 990}$$

Multiply 420 and 530 to get 222600.

$$\frac{\frac{\left(272600-222600\right)^{2}}{500}}{1110\times 990}$$

Subtract 222600 from 272600 to get 50000.

$$\frac{\frac{50000^{2}}{500}}{1110\times 990}$$

Calculate 50000 to the power of 2 and get 2500000000.

$$\frac{\frac{2500000000}{500}}{1110\times 990}$$

Divide 2500000000 by 500 to get 5000000.

$$\frac{5000000}{1110\times 990}$$

Multiply 1110 and 990 to get 1098900.

$$\frac{5000000}{1098900}$$

Reduce the fraction \frac{5000000}{1098900} to lowest terms by extracting and canceling out 100.

$$\frac{50000}{10989}$$

Factor

$$\frac{2 ^ {4} \cdot 5 ^ {5}}{3 ^ {3} \cdot 11 \cdot 37} = 4\frac{6044}{10989} = 4.55000455000455$$