Answer
-1
Work Step by Step
Since $j=\sqrt{-1}$, $j^2=-1$, $j^3=-j$, $j^4=1$, then by multiplying both the denominator and numerator by $j^2$, we have
$$ \frac{1}{j^6}= \frac{j^2}{j^8}=j^2=-1.$$
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