# Solve the equation step by step ?

May 23, 2018

$v = \sqrt{\frac{6.67 \cdot {10}^{-} 11 \cdot 6 \cdot {10}^{24}}{7300 \cdot {10}^{3}}} \approx 7402.70221$

#### Explanation:

Note that

$\textcolor{red}{{x}^{n} \cdot {x}^{m} = {x}^{n + m}}$

$\textcolor{red}{{x}^{n} / {x}^{m} = {x}^{n} \cdot {x}^{-} m = {x}^{n - m}}$

$v = \sqrt{\frac{6.67 \cdot {10}^{-} 11 \cdot 6 \cdot {10}^{24}}{7300 \cdot {10}^{3}}}$

$v = \sqrt{\frac{6.67 \cdot 6 \cdot {10}^{24 - 11}}{73 \cdot {10}^{5}}}$

$v = \sqrt{\frac{6.67 \cdot 6 \cdot {10}^{13} \cdot {10}^{-} 5}{73}}$

$v = \sqrt{\frac{6.67 \cdot 6 \cdot {10}^{13 - 5}}{73}}$

$v = \sqrt{\frac{6.67 \cdot 6 \cdot {10}^{8}}{73}}$

$v = \sqrt{\frac{40.02 \cdot {10}^{8}}{73}}$

$v \approx \sqrt{\left(0.548 \cdot {10}^{8}\right)}$

$v \approx 7402.70221$

in the last equation you must use calculator to get the exact value because there are complex numbers.