To find how many times \( 4 \times 10^4 \) is larger than \( 2 \times 10^2 \), you can set up the following division:
\[ \frac{4 \times 10^4}{2 \times 10^2} \]
First, simplify the constants:
\[ \frac{4}{2} = 2 \]
Now, divide the powers of ten:
\[ \frac{10^4}{10^2} = 10^{4-2} = 10^2 \]
Putting it all together, we have:
\[ \frac{4 \times 10^4}{2 \times 10^2} = 2 \times 10^2 \]
Now, \( 10^2 = 100 \), so:
\[ 2 \times 10^2 = 2 \times 100 = 200 \]
Thus, \( 4 \times 10^4 \) is 200 times larger than \( 2 \times 10^2 \).
The correct answer is 200.