Solve 40*(12*14-6*8)^2/(20*20*18*22)

$$\frac { 40 \times ( 12 \times 14 - 6 \times 8 ) ^ { 2 } } { ( 20 \times 20 \times 18 \times 22 ) }$$

Evaluate

$$\frac{40}{11}\approx 3.636363636$$

Solution Steps

Cancel out 2\times 20 in both numerator and denominator.

$$\frac{\left(12\times 14-6\times 8\right)^{2}}{10\times 18\times 22}$$

Multiply 12 and 14 to get 168.

$$\frac{\left(168-6\times 8\right)^{2}}{10\times 18\times 22}$$

Multiply 6 and 8 to get 48.

$$\frac{\left(168-48\right)^{2}}{10\times 18\times 22}$$

Subtract 48 from 168 to get 120.

$$\frac{120^{2}}{10\times 18\times 22}$$

Calculate 120 to the power of 2 and get 14400.

$$\frac{14400}{10\times 18\times 22}$$

Multiply 10 and 18 to get 180.

$$\frac{14400}{180\times 22}$$

Multiply 180 and 22 to get 3960.

$$\frac{14400}{3960}$$

Reduce the fraction \frac{14400}{3960} to lowest terms by extracting and canceling out 360.

$$\frac{40}{11}$$

Factor

$$\frac{2 ^ {3} \cdot 5}{11} = 3\frac{7}{11} = 3.6363636363636362$$