The problem reads:

"A certain star is $5.4 \times 10^2$ light years from the Earth. One light year is about $5.9 \times 10^{12}$ miles. How far from the Earth (in miles) is the star?"

Solution:

To find how far the star is in miles, we multiply the number of light years by the distance in miles per light year:

$\text{Distance in miles} = \text{Number of light years} \times \text{Distance per light year}$

$\text{Distance in miles} = (5.4 \times 10^2) \times (5.9 \times 10^{12})$

Now, simplify:

$\text{Distance in miles} = 5.4 \times 5.9 \times 10^{2 + 12} = 31.86 \times 10^{14}$

$\text{Distance in miles} = 3.186 \times 10^{15} \text{ miles}$

So, the star is approximately $3.186 \times 10^{15}$ miles from the Earth.

Would you like further details or have any questions?

Here are some related questions you can consider:

1. What is a light year and how is it defined in astronomy?
2. How do you perform multiplication with numbers in scientific notation?
3. How far is the nearest star to Earth in light years and miles?
4. What is the difference between light years and astronomical units (AU)?
5. How do astronomers measure distances to stars?

Tip: When multiplying numbers in scientific notation, remember to handle the base and exponent separately. Multiply the coefficients and add the exponents for an efficient calculation.