Solve 4*107.9/6.022*10^23*(408.6*10^-10)^3

$$\frac { 4 \times 107.9 } { 6.022 \times 10 ^ { 23 } \times ( 408.6 \times 10 ^ { - 10 } ) ^ { 3 } }$$

Evaluate

$$\frac{269750000000000}{25675319429577}\approx 10.506198403$$

Solution Steps

Multiply 4 and 107.9 to get 431.6.

$$\frac{431.6}{6.022\times 10^{23}\times \left(408.6\times 10^{-10}\right)^{3}}$$

Calculate 10 to the power of 23 and get 100000000000000000000000.

$$\frac{431.6}{6.022\times 100000000000000000000000\times \left(408.6\times 10^{-10}\right)^{3}}$$

Multiply 6.022 and 100000000000000000000000 to get 602200000000000000000000.

$$\frac{431.6}{602200000000000000000000\times \left(408.6\times 10^{-10}\right)^{3}}$$

Calculate 10 to the power of -10 and get \frac{1}{10000000000}.

$$\frac{431.6}{602200000000000000000000\times \left(408.6\times \frac{1}{10000000000}\right)^{3}}$$

Multiply 408.6 and \frac{1}{10000000000} to get \frac{2043}{50000000000}.

$$\frac{431.6}{602200000000000000000000\times \left(\frac{2043}{50000000000}\right)^{3}}$$

Calculate \frac{2043}{50000000000} to the power of 3 and get \frac{8527173507}{125000000000000000000000000000000}.

$$\frac{431.6}{602200000000000000000000\times \frac{8527173507}{125000000000000000000000000000000}}$$

Multiply 602200000000000000000000 and \frac{8527173507}{125000000000000000000000000000000} to get \frac{25675319429577}{625000000000}.

$$\frac{431.6}{\frac{25675319429577}{625000000000}}$$

Divide 431.6 by \frac{25675319429577}{625000000000} by multiplying 431.6 by the reciprocal of \frac{25675319429577}{625000000000}.

$$431.6\times \frac{625000000000}{25675319429577}$$

Multiply 431.6 and \frac{625000000000}{25675319429577} to get \frac{269750000000000}{25675319429577}.

$$\frac{269750000000000}{25675319429577}$$

Factor

$$\frac{13 \cdot 83 \cdot 2 ^ {10} \cdot 5 ^ {12}}{3011 \cdot 3 ^ {6} \cdot 227 ^ {3}} = 10\frac{12996805704230}{25675319429577} = 10.506198403485417$$