To find out how many times larger \( (1.176 \times 10^1) \) is than \( (8 \times 10^{-1}) \), we can set up the following division:
\[ \frac{1.176 \times 10^1}{8 \times 10^{-1}} \]
First, we can simplify the expression step by step.
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Calculate the numerical part: \[ \frac{1.176}{8} = 0.147 \]
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Calculate the powers of ten: \[ \frac{10^1}{10^{-1}} = 10^{1 - (-1)} = 10^{1 + 1} = 10^2 = 100 \]
Now we can multiply the two results:
\[ 0.147 \times 100 = 14.7 \]
Thus, \( (1.176 \times 10^1) \) is 14.7 times larger than \( (8 \times 10^{-1}) \).
The answer is \( \boxed{14.7} \).