Question 143735
{{{i^16}}} Start with the given expression



{{{i^(4*4)}}} Rewrite 16 as 4*4



{{{(i^4)^4}}} Rewrite the expression using the identity {{{x^(y*z)=(x^y)^z}}}



{{{(1)^4}}} Evaluate {{{i^4}}} to get 1. note: remember, {{{i^2=-1}}}. So {{{i^4=(i^2)^2=(-1)^2=1}}}



{{{1}}} Raise 1 to the fourth power to get 1



So {{{i^16=1}}}