How many times is 4 × 10^4 larger than 2 × 10^2 ?(1 point)

Question

Responses

200
200

20
20

2
2

2,000

Answer 1

To determine how many times \( 4 \times 10^4 \) is larger than \( 2 \times 10^2 \), we can divide the two quantities:

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

First, simplify the fraction:

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

Calculating each part:

1. \(\frac{4}{2} = 2\)
2. Using the property of exponents \(\frac{10^4}{10^2} = 10^{4-2} = 10^2\)

Now combine the results:

\[ 2 \times 10^2 = 2 \times 100 = 200 \]

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

The answer is 200.