Answer:
The distance, in light-years, from Earth to the star is 4.33 light- years.
Step-by-step explanation:
As given
Distances in space are measured in light-years.
\(The\ distance\ from\ Earth\ to\ a\ star\ is\ 4.1\times 10^{13}\kilometers.\)
\(1 light-year = 9.46\times 10^{12}\ kilometers\)
As
\(1\ kilometer = \frac{1}{9.46\times 10^{12}} \ light\ years\)
Thus
\(4.1\times 10^{13}\ kilometer = \frac{4.1\times 10^{13}}{9.46\times 10^{12}} \ light\ years\)
by using the exponent property .
\(\frac{x^{a}}{x^{b}} = x^{a-b}\)
\(4.1\times 10^{13}\ kilometer =0.433\times 10^{13-12} \ light\ years\)
\(4.1\times 10^{13}\ kilometer =0.433\times 10^{1} \ light\ years\)
\(4.1\times 10^{13}\ kilometer =\frac{433}{1000} \times 10^{1} \ light\ years\)
\(4.1\times 10^{13}\ kilometer =\frac{433}{100}\ light\ years\)
\(4.1\times 10^{13}\ kilometer = 4.33\ light\ years\)
Therefore the distance, in light-years, from Earth to the star is 4.33 light- years.
