Solve frac{4*3.14^{2}*(1.2*10^9)^2}{6.67*10^-11*(16*24*3600)^2}

$$\frac { 4 \times 3.14 ^ { 2 } \times ( 1.2 \times 10 ^ { 9 } ) ^ { 2 } } { 6.67 \times 10 ^ { - 11 } \times ( 16 \times 24 \times 3600 ) ^ { 2 } }$$

Evaluate

$$\frac{24071289062500000000000}{54027}\approx 4.455418413 \cdot 10^{17}$$

Solution Steps

Calculate 3.14 to the power of 2 and get 9.8596.

$$\frac{4\times 9.8596\times \left(1.2\times 10^{9}\right)^{2}}{6.67\times 10^{-11}\times \left(16\times 24\times 3600\right)^{2}}$$

Multiply 4 and 9.8596 to get 39.4384.

$$\frac{39.4384\times \left(1.2\times 10^{9}\right)^{2}}{6.67\times 10^{-11}\times \left(16\times 24\times 3600\right)^{2}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{39.4384\times \left(1.2\times 1000000000\right)^{2}}{6.67\times 10^{-11}\times \left(16\times 24\times 3600\right)^{2}}$$

Multiply 1.2 and 1000000000 to get 1200000000.

$$\frac{39.4384\times 1200000000^{2}}{6.67\times 10^{-11}\times \left(16\times 24\times 3600\right)^{2}}$$

Calculate 1200000000 to the power of 2 and get 1440000000000000000.

$$\frac{39.4384\times 1440000000000000000}{6.67\times 10^{-11}\times \left(16\times 24\times 3600\right)^{2}}$$

Multiply 39.4384 and 1440000000000000000 to get 56791296000000000000.

$$\frac{56791296000000000000}{6.67\times 10^{-11}\times \left(16\times 24\times 3600\right)^{2}}$$

Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

$$\frac{56791296000000000000}{6.67\times \frac{1}{100000000000}\times \left(16\times 24\times 3600\right)^{2}}$$

Multiply 6.67 and \frac{1}{100000000000} to get \frac{667}{10000000000000}.

$$\frac{56791296000000000000}{\frac{667}{10000000000000}\times \left(16\times 24\times 3600\right)^{2}}$$

Multiply 16 and 24 to get 384.

$$\frac{56791296000000000000}{\frac{667}{10000000000000}\times \left(384\times 3600\right)^{2}}$$

Multiply 384 and 3600 to get 1382400.

$$\frac{56791296000000000000}{\frac{667}{10000000000000}\times 1382400^{2}}$$

Calculate 1382400 to the power of 2 and get 1911029760000.

$$\frac{56791296000000000000}{\frac{667}{10000000000000}\times 1911029760000}$$

Multiply \frac{667}{10000000000000} and 1911029760000 to get \frac{248956416}{1953125}.

$$\frac{56791296000000000000}{\frac{248956416}{1953125}}$$

Divide 56791296000000000000 by \frac{248956416}{1953125} by multiplying 56791296000000000000 by the reciprocal of \frac{248956416}{1953125}.

$$56791296000000000000\times \frac{1953125}{248956416}$$

Multiply 56791296000000000000 and \frac{1953125}{248956416} to get \frac{24071289062500000000000}{54027}.

$$\frac{24071289062500000000000}{54027}$$

Factor

$$\frac{2 ^ {11} \cdot 5 ^ {21} \cdot 157 ^ {2}}{23 \cdot 29 \cdot 3 ^ {4}} = 4.455418413478445 \times 10^{17}\frac{39462}{54027} = 4.455418413478445 \times 10^{17}$$