Question

in a science fiction book, the mongo nebula is about 8 × 10³ light - years away from the planet hegula. one light year is equal to approximately 6 × 10¹² miles. what is the approximate distance, in miles, between hegula and the mongo nebula? o1.4 × 10¹⁶ miles o4.8 × 10¹⁵ miles o4.8 × 10³⁷ miles o4.8 × 10¹⁶ miles

Explanation:

Step1: Identify given values

One light - year is approximately $6\times10^{12}$ miles and the distance in light - years is $8\times 10^{3}$ light - years.

Step2: Use multiplication formula for distance

The distance $d$ in miles is the product of the number of light - years and the number of miles in one light - year. So $d=(6\times 10^{12})\times(8\times 10^{3})$.

Step3: Apply multiplication rule of exponents

According to the rule $a^{m}\times a^{n}=a^{m + n}$ and $(a\times b)\times(c\times d)=(a\times c)\times(b\times d)$. We have $(6\times 10^{12})\times(8\times 10^{3})=(6\times8)\times(10^{12}\times10^{3}) = 48\times10^{12 + 3}=48\times10^{15}$.

Step4: Convert to scientific notation

$48\times10^{15}=4.8\times10^{16}$ (since $48 = 4.8\times10^{1}$ and $4.8\times10^{1}\times10^{15}=4.8\times10^{1+15}$).

Answer:

$4.8\times 10^{16}$ miles