6.7×10^-11×6×10^24×7.4×10^22÷(3.84×10^8)^2

asked by guest
on Jan 24, 2025 at 3:27 am



You asked:

Evaluate the expression: \(\frac{6.7 \cdot {10}^{-11} \cdot 6 \cdot {10}^{24} \cdot 7.4 \cdot {10}^{22}}{{\left( 3.84 \cdot {10}^{8} \right)}^{2}}\)

MathBot Answer:

\[\frac{6.7 \cdot {10}^{-11} \cdot 6 \cdot {10}^{24} \cdot 7.4 \cdot {10}^{22}}{{\left( 3.84 \cdot {10}^{8} \right)}^{2}} = \frac{605224609375000000000}{3} = 201741536458333333333.\overline{3}\]

\[\begin{aligned}\frac{6.7 \cdot {10}^{-11} \cdot 6 \cdot {10}^{24} \cdot 7.4 \cdot {10}^{22}}{{\left( 3.84 \cdot {10}^{8} \right)}^{2}}& = \left(6 + \frac{7}{10}\right) \cdot \frac{1}{10^{11}} \cdot 6 \cdot 10^{24} \cdot \left(7 + \frac{4}{10}\right) \cdot 10^{22} \cdot \frac{1}{\left(\left(3 + \frac{84}{100}\right) \cdot 10^{8}\right)^{2}}\\& = \frac{67}{10} \cdot \frac{1}{10^{11}} \cdot 6 \cdot 10^{24} \cdot \left(7 + \frac{4}{10}\right) \cdot 10^{22} \cdot \frac{1}{\left(\left(3 + \frac{84}{100}\right) \cdot 10^{8}\right)^{2}}\\& = \frac{67}{10} \cdot \frac{6}{100000000000} \cdot 10^{24} \cdot \left(7 + \frac{4}{10}\right) \cdot 10^{22} \cdot \frac{1}{\left(\left(3 + \frac{84}{100}\right) \cdot 10^{8}\right)^{2}}\\& = \frac{67}{10} \cdot \frac{6}{100000000000} \cdot 1000000000000000000000000 \cdot \left(7 + \frac{4}{10}\right) \cdot 10^{22} \cdot \frac{1}{\left(\left(3 + \frac{84}{100}\right) \cdot 10^{8}\right)^{2}}\\& = \frac{67}{10} \cdot \frac{6}{100000000000} \cdot 1000000000000000000000000 \cdot \left(7 + \frac{2}{5}\right) \cdot 10^{22} \cdot \frac{1}{\left(\left(3 + \frac{84}{100}\right) \cdot 10^{8}\right)^{2}}\\& = \frac{67}{10} \cdot \frac{6}{100000000000} \cdot 1000000000000000000000000 \cdot \frac{37}{5} \cdot 10^{22} \cdot \frac{1}{\left(\left(3 + \frac{84}{100}\right) \cdot 10^{8}\right)^{2}}\\& = \frac{67}{10} \cdot \frac{6}{100000000000} \cdot 1000000000000000000000000 \cdot \frac{37}{5} \cdot 10000000000000000000000 \cdot \frac{1}{\left(\left(3 + \frac{84}{100}\right) \cdot 10^{8}\right)^{2}}\\& = \frac{67}{10} \cdot \frac{6}{100000000000} \cdot 1000000000000000000000000 \cdot \frac{37}{5} \cdot 10000000000000000000000 \cdot \frac{1}{\left(\left(3 + \frac{21}{25}\right) \cdot 10^{8}\right)^{2}}\\& = \frac{67}{10} \cdot \frac{6}{100000000000} \cdot 1000000000000000000000000 \cdot \frac{37}{5} \cdot 10000000000000000000000 \cdot \frac{1}{\left(\frac{96}{25} \cdot 10^{8}\right)^{2}}\\& = \frac{67}{10} \cdot \frac{6}{100000000000} \cdot 1000000000000000000000000 \cdot \frac{37}{5} \cdot 10000000000000000000000 \cdot \frac{1}{\left(\frac{96}{25} \cdot 100000000\right)^{2}}\\& = \frac{67}{10} \cdot \frac{6}{100000000000} \cdot 1000000000000000000000000 \cdot \frac{37}{5} \cdot 10000000000000000000000 \cdot \frac{1}{384000000^{2}}\\& = \frac{67}{10} \cdot \frac{6}{100000000000} \cdot 1000000000000000000000000 \cdot \frac{37}{5} \cdot \frac{10000000000000000000000}{147456000000000000}\\& = \frac{67}{10} \cdot \frac{6}{100000000000} \cdot 1000000000000000000000000 \cdot \frac{37}{5} \cdot \frac{9765625}{144}\\& = \frac{67}{1000000000000} \cdot 6 \cdot 1000000000000000000000000 \cdot \frac{37}{5} \cdot \frac{9765625}{144}\\& = \frac{201}{500000000000} \cdot 1000000000000000000000000 \cdot \frac{37}{5} \cdot \frac{9765625}{144}\\& = 402000000000000 \cdot \frac{37}{5} \cdot \frac{9765625}{144}\\& = 2974800000000000 \cdot \frac{9765625}{144}\\& = \frac{605224609375000000000}{3}\end{aligned}\]

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