Answer:
[tex]\boxed{\bold{-1}}[/tex]
Step By Step Explanation:
Apply Exponent Rule [tex]\bold{a^{bc}=\left(a^b\right)^c}[/tex]
[tex]\bold{i^{38}=\left(i^2\right)^{19}}[/tex]
[tex]\bold{\left(i^2\right)^{19}}[/tex]
Apply Imaginary number Rule [tex]\bold{\:i^2=-1}[/tex]
[tex]\bold{\left(-1\right)^{19}}[/tex]
Apply Exponent Rule [tex]\bold{\left(-a\right)^n=-a^n,\:\mathrm{if\:}n\mathrm{\:is\:odd}}[/tex]
[tex]\bold{\left(-1\right)^{19}=-1^{19}}[/tex]
[tex]\bold{-1^{19}}[/tex]
Solve [tex]\bold{1^{19}=1}[/tex]
[tex]\bold{-1}[/tex]
Regards,
Mordancy
