Multiply.

Question

(7.1×104)⋅(4.8×103)

Responses

3.408×107​
3.408 cross times 10 to the power of 7 ​

3.408×108
3.408 cross times 10 to the power of 8

3.408×1012​
3.408 cross times 10 to the power of 12 ​

3.408×1013​
3.408 cross times 10 to the power of 13 ​

Answer 1

To multiply the numbers \( (7.1 \times 10^4) \) and \( (4.8 \times 10^3) \), we can follow these steps:

1. Multiply the decimal parts: \[ 7.1 \times 4.8 = 34.08 \]

2. Multiply the powers of 10: \[ 10^4 \times 10^3 = 10^{4+3} = 10^7 \]

3. Combine the results: \[ 34.08 \times 10^7 \]

Since scientific notation typically formats the leading number to be between 1 and 10, we convert \( 34.08 \) to \( 3.408 \) by moving the decimal point one place to the left, which means we need to increase the exponent by 1: \[ 34.08 \times 10^7 = 3.408 \times 10^8 \]

Thus, the final result is: \[ \boxed{3.408 \times 10^8} \]