Answer
$=-i$
Work Step by Step
Apply exponent rule: $\displaystyle \quad a^{-n}=\frac{1}{a^{n}}$
$\displaystyle \frac{1}{i^{-11}}=\frac{1}{(\frac{1}{i^{11}})}=i^{11}$
$ i^{11}=i^{10+1}\qquad$...Apply exponent rule: $\quad a^{m+n}=a^{m}a^{n}$
$=i^{10}i\qquad$...Apply exponent rule: $\quad a^{mn}=(a^{m})^{n},\ i^{10}=(i^{2})^{5}$
$=i(i^{2})^{5}\qquad$...Apply imaginary number rule: $\quad i^{2}=-1$
$=(-1)^{5}i\qquad$...Apply exponent rule: $(-a)^{n}=-a^{n},$ if $n$ is odd
$=-1^{5}i
$=-1i$\qquad$...Multiply: $1i=i$
$=-i$
