ISTANCE A long-distance runner runs $$ 2^{5} $$ miles one week and $$ 2^{7} $$ miles the next week How many times farther did he run in the second week than in the first week?

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The distance run in the first week is $$2^5$$ miles, and in the second week it is $$2^7$$ miles.

To determine how many times farther the runner ran in the second week compared to the first week, we calculate the ratio:

$$
\frac{2^7}{2^5}
$$

Using the quotient rule for exponents, where $$\frac{a^m}{a^n} = a^{m-n}$$, we have:

$$
\frac{2^7}{2^5} = 2^{7-5} = 2^2 = 4.
$$

Thus, the runner ran 4 times as far in the second week as in the first week.
The runner ran 4 times farther in the second week than in the first week.

ISTANCE A long-distance runner runs miles one week and miles the next week
How many times farther did he run in the second week than in the first week?

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ISTANCE A long-distance runner runs miles one week and miles the next week How many times farther did he run in the second week than in the first week?