To determine how many times \( 4 \times 10^4 \) is larger than \( 2 \times 10^2 \), we can divide the two numbers:
\[ \frac{4 \times 10^4}{2 \times 10^2} \]
This can be simplified step by step:
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Divide the coefficients (4 and 2): \[ \frac{4}{2} = 2 \]
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Divide the powers of 10: \[ \frac{10^4}{10^2} = 10^{4-2} = 10^2 \]
Now, combine the results: \[ 2 \times 10^2 \]
Since \( 10^2 = 100 \): \[ 2 \times 100 = 200 \]
Thus, \( 4 \times 10^4 \) is \( 200 \) times larger than \( 2 \times 10^2 \).
The answer is \( 200 \).