(6.673 ∗ 10^-11 ∗ 5.98 ∗ 10^24 ∗1.99∗10^30)/(160∗10^9)^2

asked by guest
on Nov 27, 2024 at 7:25 pm



You asked:

Evaluate the expression: \(\frac{6.673 \cdot {10}^{-11} \cdot 5.98 \cdot {10}^{24} \cdot 1.99 \cdot {10}^{30}}{{\left( 160 \cdot {10}^{9} \right)}^{2}}\)

MathBot Answer:

\[\frac{6.673 \cdot {10}^{-11} \cdot 5.98 \cdot {10}^{24} \cdot 1.99 \cdot {10}^{30}}{{\left( 160 \cdot {10}^{9} \right)}^{2}} = 31019544765625000000000\]

\[\begin{aligned}\frac{6.673 \cdot {10}^{-11} \cdot 5.98 \cdot {10}^{24} \cdot 1.99 \cdot {10}^{30}}{{\left( 160 \cdot {10}^{9} \right)}^{2}}& = \left(6 + \frac{673}{1000}\right) \cdot \frac{1}{10^{11}} \cdot \left(5 + \frac{98}{100}\right) \cdot 10^{24} \cdot \left(1 + \frac{99}{100}\right) \cdot 10^{30} \cdot \frac{1}{\left(160 \cdot 10^{9}\right)^{2}}\\& = \frac{6673}{1000} \cdot \frac{1}{10^{11}} \cdot \left(5 + \frac{98}{100}\right) \cdot 10^{24} \cdot \left(1 + \frac{99}{100}\right) \cdot 10^{30} \cdot \frac{1}{\left(160 \cdot 10^{9}\right)^{2}}\\& = \frac{6673}{1000} \cdot \frac{1}{100000000000} \cdot \left(5 + \frac{98}{100}\right) \cdot 10^{24} \cdot \left(1 + \frac{99}{100}\right) \cdot 10^{30} \cdot \frac{1}{\left(160 \cdot 10^{9}\right)^{2}}\\& = \frac{6673}{1000} \cdot \frac{1}{100000000000} \cdot \left(5 + \frac{49}{50}\right) \cdot 10^{24} \cdot \left(1 + \frac{99}{100}\right) \cdot 10^{30} \cdot \frac{1}{\left(160 \cdot 10^{9}\right)^{2}}\\& = \frac{6673}{1000} \cdot \frac{1}{100000000000} \cdot \frac{299}{50} \cdot 10^{24} \cdot \left(1 + \frac{99}{100}\right) \cdot 10^{30} \cdot \frac{1}{\left(160 \cdot 10^{9}\right)^{2}}\\& = \frac{6673}{1000} \cdot \frac{1}{100000000000} \cdot \frac{299}{50} \cdot 1000000000000000000000000 \cdot \left(1 + \frac{99}{100}\right) \cdot 10^{30} \cdot \frac{1}{\left(160 \cdot 10^{9}\right)^{2}}\\& = \frac{6673}{1000} \cdot \frac{1}{100000000000} \cdot \frac{299}{50} \cdot 1000000000000000000000000 \cdot \frac{199}{100} \cdot 10^{30} \cdot \frac{1}{\left(160 \cdot 10^{9}\right)^{2}}\\& = \frac{6673}{1000} \cdot \frac{1}{100000000000} \cdot \frac{299}{50} \cdot 1000000000000000000000000 \cdot \frac{199}{100} \cdot 1000000000000000000000000000000 \cdot \frac{1}{\left(160 \cdot 10^{9}\right)^{2}}\\& = \frac{6673}{1000} \cdot \frac{1}{100000000000} \cdot \frac{299}{50} \cdot 1000000000000000000000000 \cdot \frac{199}{100} \cdot 1000000000000000000000000000000 \cdot \frac{1}{\left(160 \cdot 1000000000\right)^{2}}\\& = \frac{6673}{1000} \cdot \frac{1}{100000000000} \cdot \frac{299}{50} \cdot 1000000000000000000000000 \cdot \frac{199}{100} \cdot 1000000000000000000000000000000 \cdot \frac{1}{160000000000^{2}}\\& = \frac{6673}{1000} \cdot \frac{1}{100000000000} \cdot \frac{299}{50} \cdot 1000000000000000000000000 \cdot \frac{199}{100} \cdot \frac{1000000000000000000000000000000}{25600000000000000000000}\\& = \frac{6673}{1000} \cdot \frac{1}{100000000000} \cdot \frac{299}{50} \cdot 1000000000000000000000000 \cdot \frac{199}{100} \cdot 39062500\\& = \frac{6673}{100000000000000} \cdot \frac{299}{50} \cdot 1000000000000000000000000 \cdot \frac{199}{100} \cdot 39062500\\& = \frac{1995227}{5000000000000000} \cdot 1000000000000000000000000 \cdot \frac{199}{100} \cdot 39062500\\& = 399045400000000 \cdot \frac{199}{100} \cdot 39062500\\& = 794100346000000 \cdot 39062500\\& = 31019544765625000000000\end{aligned}\]

+ Submit Question