Solve 400div6*0.16^2div0.5div0.53

$$400 \div 6 \times { 0.16 }^{ 2 } \div 0.5 \div 0.53$$

Evaluate

$$\frac{1024}{159}\approx 6.440251572$$

Solution Steps

Express \frac{\frac{\frac{400}{6}\times 0.16^{2}}{0.5}}{0.53} as a single fraction.

$$\frac{\frac{400}{6}\times 0.16^{2}}{0.5\times 0.53}$$

Reduce the fraction \frac{400}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{200}{3}\times 0.16^{2}}{0.5\times 0.53}$$

Calculate 0.16 to the power of 2 and get 0.0256.

$$\frac{\frac{200}{3}\times 0.0256}{0.5\times 0.53}$$

Convert decimal number 0.0256 to fraction \frac{256}{10000}. Reduce the fraction \frac{256}{10000} to lowest terms by extracting and canceling out 16.

$$\frac{\frac{200}{3}\times \frac{16}{625}}{0.5\times 0.53}$$

Multiply \frac{200}{3} times \frac{16}{625} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{200\times 16}{3\times 625}}{0.5\times 0.53}$$

Do the multiplications in the fraction \frac{200\times 16}{3\times 625}.

$$\frac{\frac{3200}{1875}}{0.5\times 0.53}$$

Reduce the fraction \frac{3200}{1875} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{128}{75}}{0.5\times 0.53}$$

Multiply 0.5 and 0.53 to get 0.265.

$$\frac{\frac{128}{75}}{0.265}$$

Express \frac{\frac{128}{75}}{0.265} as a single fraction.

$$\frac{128}{75\times 0.265}$$

Multiply 75 and 0.265 to get 19.875.

$$\frac{128}{19.875}$$

Expand \frac{128}{19.875} by multiplying both numerator and the denominator by 1000.

$$\frac{128000}{19875}$$

Reduce the fraction \frac{128000}{19875} to lowest terms by extracting and canceling out 125.

$$\frac{1024}{159}$$

Factor

$$\frac{2 ^ {10}}{3 \cdot 53} = 6\frac{70}{159} = 6.440251572327044$$