To multiply the numbers \(3.92 \times 10^7\) and \(7.87 \times 10^9\) in scientific notation, you can follow these steps:
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Multiply the coefficients (the numbers before the powers of ten): \[ 3.92 \times 7.87 = 30.8704 \]
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Add the exponents of the powers of ten: \[ 10^7 \times 10^9 = 10^{7 + 9} = 10^{16} \]
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Combine the results: \[ 30.8704 \times 10^{16} \]
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Convert \(30.8704\) to scientific notation. Since \(30.8704\) is greater than 10, we can express it as \(3.08704 \times 10^1\): \[ 30.8704 \times 10^{16} = 3.08704 \times 10^1 \times 10^{16} = 3.08704 \times 10^{17} \]
So, the final result in scientific notation is: \[ \boxed{3.08704 \times 10^{17}} \]