Question 179689
First, rewrite the expression to get rid of the negative exponent. Simply flip the fraction to get: {{{i^(-33)=1/i^33}}}



Now divide 33 into 4 to get 8 remainder 1



Since we get a remainder 1, this tells us that {{{i^33=i}}}



So {{{i^(-33)=1/i^33=1/i}}}



{{{1/i}}} Start with the given expression.



{{{(1/i)(i/i)}}} Multiply the fraction by {{{i/i}}}



{{{(1*i)/(i*i)}}} Combine the fractions



{{{(i)/(i^2)}}} Multiply



{{{(i)/(-1)}}} Replace {{{i^2}}} with -1 (since {{{i^2=-1}}})



{{{-i}}} Reduce



So {{{i^(-33)=1/i^33=1/i=-i}}}



or more simply {{{i^(-33)=-i}}}