Question

Question #8e2b3

Answer 1

`-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`