To determine how many times \(4 \times 10^4\) is larger than \(2 \times 10^2\), we can divide the two expressions.
Let's calculate it:
\[ \frac{4 \times 10^4}{2 \times 10^2} \]
This can be simplified by breaking it down:
- First, simplify the constants:
\[ \frac{4}{2} = 2 \]
- Then, simplify the powers of 10:
\[ \frac{10^4}{10^2} = 10^{4-2} = 10^2 \]
- Putting it all together:
\[ \frac{4 \times 10^4}{2 \times 10^2} = 2 \times 10^2 \]
Now we can determine the result of \(2 \times 10^2\):
\[ 2 \times 10^2 = 2 \times 100 = 200 \]
Therefore, \(4 \times 10^4\) is \(200\) times larger than \(2 \times 10^2\).