SOLUTION: How do you simplify i^-33. I'm not sure how to deal with the negative exponent. Please help.

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Question 179689: How do you simplify i^-33. I'm not sure how to deal with the negative exponent. Please help.
Found 2 solutions by jim_thompson5910, Mathtut:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, rewrite the expression to get rid of the negative exponent. Simply flip the fraction to get: i%5E%28-33%29=1%2Fi%5E33


Now divide 33 into 4 to get 8 remainder 1


Since we get a remainder 1, this tells us that i%5E33=i


So i%5E%28-33%29=1%2Fi%5E33=1%2Fi


1%2Fi Start with the given expression.


%281%2Fi%29%28i%2Fi%29 Multiply the fraction by i%2Fi


%281%2Ai%29%2F%28i%2Ai%29 Combine the fractions


%28i%29%2F%28i%5E2%29 Multiply


%28i%29%2F%28-1%29 Replace i%5E2 with -1 (since i%5E2=-1)


-i Reduce


So i%5E%28-33%29=1%2Fi%5E33=1%2Fi=-i


or more simply i%5E%28-33%29=-i

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
i%5E32=1 i%5E1=i
:
i%5E%28-33%29=1%2Fi%5E33=1%2Fi%5E32i%5E1=1%2F%281%29%28i%29=highlight%281%2Fi%29
:
1/i
:
multiply top and bottom by -i
:
-i%2F%28-i%5E2%29=%28-i%29%2F1=highlight%28-i%29