Solve 90*(12*20-18*40)^2/52*38*30*60=

$$\frac { 90 \times ( 12 \times 20 - 18 \times 40 ) ^ { 2 } } { 52 \times 38 \times 30 \times 60 } =$$

Evaluate

$$\frac{1440}{247}\approx 5.829959514$$

Solution Steps

Cancel out 2\times 3\times 15 in both numerator and denominator.

$$\frac{\left(12\times 20-18\times 40\right)^{2}}{2\times 20\times 26\times 38}$$

Multiply 12 and 20 to get 240.

$$\frac{\left(240-18\times 40\right)^{2}}{2\times 20\times 26\times 38}$$

Multiply 18 and 40 to get 720.

$$\frac{\left(240-720\right)^{2}}{2\times 20\times 26\times 38}$$

Subtract 720 from 240 to get -480.

$$\frac{\left(-480\right)^{2}}{2\times 20\times 26\times 38}$$

Calculate -480 to the power of 2 and get 230400.

$$\frac{230400}{2\times 20\times 26\times 38}$$

Multiply 2 and 20 to get 40.

$$\frac{230400}{40\times 26\times 38}$$

Multiply 40 and 26 to get 1040.

$$\frac{230400}{1040\times 38}$$

Multiply 1040 and 38 to get 39520.

$$\frac{230400}{39520}$$

Reduce the fraction \frac{230400}{39520} to lowest terms by extracting and canceling out 160.

$$\frac{1440}{247}$$

Factor

$$\frac{2 ^ {5} \cdot 3 ^ {2} \cdot 5}{13 \cdot 19} = 5\frac{205}{247} = 5.82995951417004$$