Respuesta :
Option B
The number of light years in [tex]6.79 \times 10^{16}[/tex] miles is 11508 light years
Solution:
Given that,
One light-year equals 5.9 x 10^12 miles
Therefore,
[tex]1 \text{ light year } = 5.9 \times 10^{12} \text{ miles }[/tex]
To find: Number of light years in [tex]6.79 \times 10^{16}[/tex] miles
Let "x" be the number of light years in [tex]6.79 \times 10^{16}[/tex] miles
Then number of light years in [tex]6.79 \times 10^{16}[/tex] miles can be found by dividing [tex]6.79 \times 10^{16}[/tex] miles by miles in 1 light year
[tex]\text{Number of light years in } 6.79 \times 10^{16} miles = \frac{6.79 \times 10^{16}}{5.9 \times 10^{12}}\\\\\text{Use the law of exponent }\\\\\frac{a^m}{a^n} = a^{m-n}\\\\\text{Number of light years in } 6.79 \times 10^{16} miles = \frac{6.79}{5.9} \times 10^{16-12}\\\\\text{Number of light years in } 6.79 \times 10^{16} miles = 1.1508 \times 10^4\\\\\text{Number of light years in } 6.79 \times 10^{16} miles = 11508[/tex]
Thus number of light years in [tex]6.79 \times 10^{16}[/tex] miles is 11508 light years
