To multiply the numbers in scientific notation, you can multiply the coefficients (the numbers in front) and then add the exponents of the powers of 10.
Given: \[ (7 \times 10^{-2}) \times (4 \times 10^{12}) \]
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Multiply the coefficients: \[ 7 \times 4 = 28 \]
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Add the exponents: \[ -2 + 12 = 10 \]
Now, combine the results: \[ 28 \times 10^{10} \]
Next, we should express \(28\) in scientific notation. \(28\) can be written as \(2.8 \times 10^1\), so we adjust the expression accordingly: \[ 28 \times 10^{10} = 2.8 \times 10^1 \times 10^{10} = 2.8 \times 10^{1+10} = 2.8 \times 10^{11} \]
Thus, the final result in scientific notation is: \[ \boxed{2.8 \times 10^{11}} \]