Math Problem Solver

\[\frac{6.67 \cdot {10}^{-11} \cdot 6 \cdot {10}^{24} \cdot 1}{{\left( 6.4 \cdot {10}^{6} \right)}^{2}} = \frac{10005}{1024} = 9.7705078125\]

\[\begin{aligned}\frac{6.67 \cdot {10}^{-11} \cdot 6 \cdot {10}^{24} \cdot 1}{{\left( 6.4 \cdot {10}^{6} \right)}^{2}}& = \left(6 + \frac{67}{100}\right) \cdot \frac{1}{10^{11}} \cdot 6 \cdot 10^{24} \cdot 1 \cdot \frac{1}{\left(\left(6 + \frac{4}{10}\right) \cdot 10^{6}\right)^{2}}\\& = \frac{667}{100} \cdot \frac{1}{10^{11}} \cdot 6 \cdot 10^{24} \cdot 1 \cdot \frac{1}{\left(\left(6 + \frac{4}{10}\right) \cdot 10^{6}\right)^{2}}\\& = \frac{667}{100} \cdot \frac{6}{100000000000} \cdot 10^{24} \cdot 1 \cdot \frac{1}{\left(\left(6 + \frac{4}{10}\right) \cdot 10^{6}\right)^{2}}\\& = \frac{667}{100} \cdot \frac{6}{100000000000} \cdot 1000000000000000000000000 \cdot 1 \cdot \frac{1}{\left(\left(6 + \frac{4}{10}\right) \cdot 10^{6}\right)^{2}}\\& = \frac{667}{100} \cdot \frac{6}{100000000000} \cdot 1000000000000000000000000 \cdot 1 \cdot \frac{1}{\left(\left(6 + \frac{2}{5}\right) \cdot 10^{6}\right)^{2}}\\& = \frac{667}{100} \cdot \frac{6}{100000000000} \cdot 1000000000000000000000000 \cdot 1 \cdot \frac{1}{\left(\frac{32}{5} \cdot 10^{6}\right)^{2}}\\& = \frac{667}{100} \cdot \frac{6}{100000000000} \cdot 1000000000000000000000000 \cdot 1 \cdot \frac{1}{\left(\frac{32}{5} \cdot 1000000\right)^{2}}\\& = \frac{667}{100} \cdot \frac{6}{100000000000} \cdot 1000000000000000000000000 \cdot 1 \cdot \frac{1}{6400000^{2}}\\& = \frac{667}{100} \cdot \frac{6}{100000000000} \cdot 1000000000000000000000000 \cdot \frac{1}{40960000000000}\\& = \frac{667}{100} \cdot \frac{6}{100000000000} \cdot \frac{1000000000000000000000000}{40960000000000}\\& = \frac{667}{10000000000000} \cdot 6 \cdot \frac{1000000000000000000000000}{40960000000000}\\& = \frac{2001}{5000000000000} \cdot \frac{1000000000000000000000000}{40960000000000}\\& = \frac{400200000000000}{40960000000000}\\& = \frac{10005}{1024}\end{aligned}\]