How do you simplify $i^333$ ?

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Answer 1 · 2016-01-13T23:04:24

$i^333=i$

Using the exponent rules:

$a^(n+m)=a^n*a^m$

$a^(n*m)=(a^n)^m$

$i^333=i*i^332=i*(i^2)^(332/2)=i*(i^2)^166$

as $i^2=-1$

$:.i*(i^2)^166=i*(-1)^166$

as $(-1)^(2p)=1$

$:.i*(-1)^166=i*1=i$

How do you simplify i^333i^333?