To solve this question, we need to find the absolute value of -1 and -9 separately, and then perform the operation indicated by the symbol in between.
The absolute value of -1 is \(1\) and the absolute value of -9 is \(9\).
The operation indicated by the symbol in between is multiplication, so we multiply the absolute values: \(1 \times 9 = 9\).
\(\boxed{9}\)
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