Question #8e2b3

1 Answer
Oct 16, 2017

-1/i

Explanation:

  • By the rule color(red)(a^(-b)=1/(a^b)

=i^(-39)=1/(1^39)

  • By the rule color(red)(a^(m*n)=(a^m)^n

=1/(1^39)=1/(i(i^2)^19

  • By the rule color(red)(i^2=-1

1/(i(i^2)^19)=1/((-1)^19i)=1/(-1^19i) [As 19 is odd]

  • As color(red)(1^19=1

1/(-1^19i)=1/-i=-1/i