Answer
$-i$
Work Step by Step
Eliminate the fraction and the negative exponent.
$\frac{1}{i^{-11}}=i^{11}$
Factor out as many $i^4$ as possible.
$i^{11}=(i^4)^{2}*i^{3}$
Know that $i^4=1$. Substitute, and simplify.
$(i^4)^{2}*i^{3}=1^{2}*i*i*i=1*-1*i=-i$