Solve frac{4*3.14^{2}*(6.8*10^{6})^3}{6.67*10^-4*(5.6*10^3)^2}

$$\frac { 4 \times 3.14 ^ { 2 } \times ( 6.8 \times 10 ^ { 6 } ) ^ { 3 } } { 6.67 \times 10 ^ { - 4 } \times ( 5.6 \times 10 ^ { 3 } ) ^ { 2 } }$$

Evaluate

$$\frac{19376085920000000000000}{32683}\approx 5.928490628 \cdot 10^{17}$$

Solution Steps

Calculate 3.14 to the power of 2 and get 9.8596.

$$\frac{4\times 9.8596\times \left(6.8\times 10^{6}\right)^{3}}{6.67\times 10^{-4}\times \left(5.6\times 10^{3}\right)^{2}}$$

Multiply 4 and 9.8596 to get 39.4384.

$$\frac{39.4384\times \left(6.8\times 10^{6}\right)^{3}}{6.67\times 10^{-4}\times \left(5.6\times 10^{3}\right)^{2}}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{39.4384\times \left(6.8\times 1000000\right)^{3}}{6.67\times 10^{-4}\times \left(5.6\times 10^{3}\right)^{2}}$$

Multiply 6.8 and 1000000 to get 6800000.

$$\frac{39.4384\times 6800000^{3}}{6.67\times 10^{-4}\times \left(5.6\times 10^{3}\right)^{2}}$$

Calculate 6800000 to the power of 3 and get 314432000000000000000.

$$\frac{39.4384\times 314432000000000000000}{6.67\times 10^{-4}\times \left(5.6\times 10^{3}\right)^{2}}$$

Multiply 39.4384 and 314432000000000000000 to get 12400694988800000000000.

$$\frac{12400694988800000000000}{6.67\times 10^{-4}\times \left(5.6\times 10^{3}\right)^{2}}$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$\frac{12400694988800000000000}{6.67\times \frac{1}{10000}\times \left(5.6\times 10^{3}\right)^{2}}$$

Multiply 6.67 and \frac{1}{10000} to get \frac{667}{1000000}.

$$\frac{12400694988800000000000}{\frac{667}{1000000}\times \left(5.6\times 10^{3}\right)^{2}}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{12400694988800000000000}{\frac{667}{1000000}\times \left(5.6\times 1000\right)^{2}}$$

Multiply 5.6 and 1000 to get 5600.

$$\frac{12400694988800000000000}{\frac{667}{1000000}\times 5600^{2}}$$

Calculate 5600 to the power of 2 and get 31360000.

$$\frac{12400694988800000000000}{\frac{667}{1000000}\times 31360000}$$

Multiply \frac{667}{1000000} and 31360000 to get \frac{522928}{25}.

$$\frac{12400694988800000000000}{\frac{522928}{25}}$$

Divide 12400694988800000000000 by \frac{522928}{25} by multiplying 12400694988800000000000 by the reciprocal of \frac{522928}{25}.

$$12400694988800000000000\times \frac{25}{522928}$$

Multiply 12400694988800000000000 and \frac{25}{522928} to get \frac{19376085920000000000000}{32683}.

$$\frac{19376085920000000000000}{32683}$$

Factor

$$\frac{2 ^ {17} \cdot 5 ^ {13} \cdot 17 ^ {3} \cdot 157 ^ {2}}{23 \cdot 29 \cdot 7 ^ {2}} = 5.92849062815531 \times 10^{17}\frac{28433}{32683} = 5.92849062815531 \times 10^{17}$$