To find how many times greater \(1.638 \times 10^{-31.638} \) is than \(6.3 \times 10^{-56.3}\), we can divide the first value by the second value.
Let's start with the numbers in scientific notation:
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The first number: \[ 1.638 \times 10^{-31.638} \]
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The second number: \[ 6.3 \times 10^{-56.3} \]
Now, we'll perform the division:
\[ \frac{1.638 \times 10^{-31.638}}{6.3 \times 10^{-56.3}} = \frac{1.638}{6.3} \times \frac{10^{-31.638}}{10^{-56.3}} \]
Calculating the numerical part:
\[ \frac{1.638}{6.3} \approx 0.25968 \]
Now calculating the exponent part:
Subtract the exponents:
\[ -31.638 - (-56.3) = -31.638 + 56.3 = 24.662 \]
Now combine both parts:
\[ 0.25968 \times 10^{24.662} \]
To express in scientific notation, we can convert \(0.25968\) into \(2.5968\) (which is within the range of \(1\) to \(10\)) and adjust the exponent accordingly:
\[ 0.25968 = 2.5968 \times 10^{-1} \]
Thus, we have:
\[ (2.5968 \times 10^{-1}) \times 10^{24.662} = 2.5968 \times 10^{24.662 - 1} = 2.5968 \times 10^{23.662} \]
Therefore, the final answer to how many times greater \(1.638 \times 10^{-31.638}\) is than \(6.3 \times 10^{-56.3}\) is:
\[ \boxed{2.5968 \times 10^{23.662}} \]