To multiply the numbers \( (7.1 \times 10^4) \) and \( (4.8 \times 10^3) \), we can follow these steps:
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Multiply the decimal parts: \[ 7.1 \times 4.8 = 34.08 \]
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Multiply the powers of 10: \[ 10^4 \times 10^3 = 10^{4+3} = 10^7 \]
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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: \[ \boxed{3.408 \times 10^8} \]