To solve \((3.2 \times 10^4) \cdot (8.03 \times 10^{-8})\), we can first multiply the coefficients (3.2 and 8.03) and then add the exponents of 10.
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Multiply the coefficients: \[ 3.2 \times 8.03 = 25.6896 \]
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Add the exponents: \[ 10^4 \times 10^{-8} = 10^{4 + (-8)} = 10^{-4} \]
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Combine the results: \[ 25.6896 \times 10^{-4} \]
Now, we can express it in scientific notation. To convert \(25.6896\) to scientific notation, we rewrite it as: \[ 2.56896 \times 10^1 \] Thus, \[ 25.6896 \times 10^{-4} = 2.56896 \times 10^{1} \times 10^{-4} = 2.56896 \times 10^{-3} \]
So, rounded to four significant figures, we get: \[ 2.5696 \times 10^{-3} \]
The correct answer is: C. \(2.5696 \times 10^{-3}\).