To multiply the numbers in scientific notation, you multiply the coefficients and add the exponents of the powers of ten.
Given: \[ (6 \times 10^{-4}) \times (3 \times 10^{12}) \]
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Multiply the coefficients: \[ 6 \times 3 = 18 \]
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Add the exponents: \[ -4 + 12 = 8 \]
Now, combine these results: \[ 18 \times 10^{8} \]
However, the coefficient 18 is not between 1 and 10, so we need to express it in proper scientific notation. This can be done by rewriting 18 as \(1.8 \times 10^{1}\):
\[ 18 \times 10^8 = 1.8 \times 10^{1} \times 10^8 \]
Now, add the exponents: \[ 1.8 \times 10^{1 + 8} = 1.8 \times 10^{9} \]
Thus, the final result in scientific notation is: \[ \boxed{1.8 \times 10^{9}} \]