To find the product of \( 69.56 \times 10^{55.6} \), we can first break it down into two parts: the numerical part, \( 69.56 \), and the exponential part, \( 10^{55.6} \).
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First, we multiply the numerical part: \[ 69 \times 5.6 = 386.4 \]
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Next, we combine this result with the exponential part: \[ 386.4 \times 10^{55.6} \]
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To express \( 386.4 \) in scientific notation, we can rewrite it as: \[ 386.4 = 3.864 \times 10^2 \]
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Now we can combine this with the exponential part: \[ 3.864 \times 10^2 \times 10^{55.6} = 3.864 \times 10^{2 + 55.6} = 3.864 \times 10^{57.6} \]
Thus, the product of \( 69 \times 5.6 \times 10^{55.6} \) expressed in scientific notation is: \[ \boxed{3.864 \times 10^{57.6}} \]