Solve 200left((80*25)-(40*55)right)^2/120*80*135*65

$$\frac{ 200 { \left((80 \times 25)-(40 \times 55) \right) }^{ 2 } }{ 120 \times 80 \times 135 \times 65 }$$

Evaluate

$$\frac{100}{1053}\approx 0.094966762$$

Solution Steps

Cancel out 5\times 40 in both numerator and denominator.

$$\frac{\left(25\times 80-40\times 55\right)^{2}}{3\times 16\times 65\times 135}$$

Multiply 25 and 80 to get 2000.

$$\frac{\left(2000-40\times 55\right)^{2}}{3\times 16\times 65\times 135}$$

Multiply 40 and 55 to get 2200.

$$\frac{\left(2000-2200\right)^{2}}{3\times 16\times 65\times 135}$$

Subtract 2200 from 2000 to get -200.

$$\frac{\left(-200\right)^{2}}{3\times 16\times 65\times 135}$$

Calculate -200 to the power of 2 and get 40000.

$$\frac{40000}{3\times 16\times 65\times 135}$$

Multiply 3 and 16 to get 48.

$$\frac{40000}{48\times 65\times 135}$$

Multiply 48 and 65 to get 3120.

$$\frac{40000}{3120\times 135}$$

Multiply 3120 and 135 to get 421200.

$$\frac{40000}{421200}$$

Reduce the fraction \frac{40000}{421200} to lowest terms by extracting and canceling out 400.

$$\frac{100}{1053}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2}}{3 ^ {4} \cdot 13} = 0.0949667616334283$$