Multiply.

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:
\[
\boxed{3.408 \times 10^8}
\]