To simplify the expression \((7 \times 10^5) \times (6 \times 10^{-3})\), we can use the properties of multiplication and exponents.
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First, multiply the coefficients (the numbers in front): \[ 7 \times 6 = 42 \]
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Next, combine the powers of ten: \[ 10^5 \times 10^{-3} = 10^{5 + (-3)} = 10^{2} \]
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Now, combine the results: \[ (7 \times 10^5) \times (6 \times 10^{-3}) = 42 \times 10^2 \]
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Finally, we can express this in proper scientific notation: \[ 42 \times 10^2 = 4.2 \times 10^3 \]
Thus, the simplified form is:
\[ \boxed{C. , 4.2 \times 10^3} \]