how many times is 4 x 10^4 larger than 2 x 10^2

To determine how many times \( 4 \times 10^4 \) is larger than \( 2 \times 10^2 \), we can divide the first number by the second number:

\[ \frac{4 \times 10^4}{2 \times 10^2} \]

Now, simplify the expression:

1. Divide the coefficients: \[ \frac{4}{2} = 2 \]

2. Divide the powers of ten: \[ \frac{10^4}{10^2} = 10^{4-2} = 10^2 \]

Now combine them:

\[ 2 \times 10^2 \]

So, \( 4 \times 10^4 \) is \( 2 \times 10^2 = 200 \) times larger than \( 2 \times 10^2 \).

Thus, \( 4 \times 10^4 \) is 200 times larger than \( 2 \times 10^2 \).