SOLUTION: 6. Simplify {{{i^16}}}

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Question 143735: 6. Simplify i%5E16
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
i%5E16 Start with the given expression


i%5E%284%2A4%29 Rewrite 16 as 4*4


%28i%5E4%29%5E4 Rewrite the expression using the identity x%5E%28y%2Az%29=%28x%5Ey%29%5Ez


%281%29%5E4 Evaluate i%5E4 to get 1. note: remember, i%5E2=-1. So i%5E4=%28i%5E2%29%5E2=%28-1%29%5E2=1


1 Raise 1 to the fourth power to get 1


So i%5E16=1