Solve 5/5{frac{5/5.56^2*0.2}}

$$\frac{ 5 }{ \frac{ 5 }{ \frac{ 5 }{ { 5.56 }^{ 2 } \times 0.2 } } }$$

Evaluate

$$\frac{15625}{19321}\approx 0.808705554$$

Solution Steps

Divide 5 by \frac{5}{\frac{5}{5.56^{2}\times 0.2}} by multiplying 5 by the reciprocal of \frac{5}{\frac{5}{5.56^{2}\times 0.2}}.

$$\frac{5\times \frac{5}{5.56^{2}\times 0.2}}{5}$$

Cancel out 5 and 5.

$$\frac{5}{5.56^{2}\times 0.2}$$

Calculate 5.56 to the power of 2 and get 30.9136.

$$\frac{5}{30.9136\times 0.2}$$

Multiply 30.9136 and 0.2 to get 6.18272.

$$\frac{5}{6.18272}$$

Expand \frac{5}{6.18272} by multiplying both numerator and the denominator by 100000.

$$\frac{500000}{618272}$$

Reduce the fraction \frac{500000}{618272} to lowest terms by extracting and canceling out 32.

$$\frac{15625}{19321}$$

Factor

$$\frac{5 ^ {6}}{139 ^ {2}} = 0.8087055535427773$$