Solve 500left(40*270-30*160right)^2/70*430*310*300

$$\frac{ 500 { \left( 40 \cdot 270-30 \cdot 160 \right) }^{ 2 } }{ 70 \cdot 430 \cdot 310 \cdot 300 }$$

Evaluate

$$\frac{60000}{9331}\approx 6.430178973$$

Solution Steps

Cancel out 5\times 10\times 10 in both numerator and denominator.

$$\frac{\left(40\times 270-30\times 160\right)^{2}}{7\times 43\times 62\times 300}$$

Multiply 40 and 270 to get 10800.

$$\frac{\left(10800-30\times 160\right)^{2}}{7\times 43\times 62\times 300}$$

Multiply 30 and 160 to get 4800.

$$\frac{\left(10800-4800\right)^{2}}{7\times 43\times 62\times 300}$$

Subtract 4800 from 10800 to get 6000.

$$\frac{6000^{2}}{7\times 43\times 62\times 300}$$

Calculate 6000 to the power of 2 and get 36000000.

$$\frac{36000000}{7\times 43\times 62\times 300}$$

Multiply 7 and 43 to get 301.

$$\frac{36000000}{301\times 62\times 300}$$

Multiply 301 and 62 to get 18662.

$$\frac{36000000}{18662\times 300}$$

Multiply 18662 and 300 to get 5598600.

$$\frac{36000000}{5598600}$$

Reduce the fraction \frac{36000000}{5598600} to lowest terms by extracting and canceling out 600.

$$\frac{60000}{9331}$$

Factor

$$\frac{2 ^ {5} \cdot 3 \cdot 5 ^ {4}}{7 \cdot 31 \cdot 43} = 6\frac{4014}{9331} = 6.430178973314757$$