The problem is asking to compare the distances of Star A and Star B and identify which one is farther away. Let's break it down.

We are given:

• Distance to Star A: $8 \times 10^4$ light years.
• Distance to Star B: $6 \times 10^7$ light years.

Step 1: Comparing the Distances

The exponent of $10$ in Star B's distance ($10^7$) is greater than that of Star A ($10^4$). This means Star B is farther away because $6 \times 10^7$ is much larger than $8 \times 10^4$.

Step 2: Calculating the Factor

To find how many times farther Star B is compared to Star A, divide the distance of Star B by the distance of Star A:

$\frac{6 \times 10^7}{8 \times 10^4} = \frac{6}{8} \times 10^{7-4} = 0.75 \times 10^3 = 750$

So, Star B is 750 times farther away than Star A.

Answer:

• Star B is farther away.
• Star B is 750 times as far as Star A.

Would you like any further clarification?

Here are 5 related questions to expand your understanding:

1. How does scientific notation help in comparing very large numbers?
2. What happens to the result if Star A’s distance was $8 \times 10^5$ light years?
3. How can we express the difference in distances between the two stars in percentage?
4. What is the importance of exponents in calculations with large numbers like this?
5. How would the calculation change if one of the numbers was much smaller, like $10^2$?

Tip: When comparing numbers in scientific notation, focus on the exponents first, as they usually indicate the larger number more clearly.