Final answer:
The runner ran 4 times farther in the second week compared to the first week.
Step-by-step explanation:
The runner ran 2⁵ miles in the first week and 2⁷ miles in the second week. To determine how many times farther the runner ran in the second week compared to the first week, we can divide the distance in the second week by the distance in the first week.
In the first week, the runner ran 2⁵ = 32 miles.
In the second week, the runner ran 2⁷ = 128 miles.
So, the runner ran 128 / 32 = 4 times farther in the second week compared to the first week.