Question 41972
Note: {{{-25 = 25i^2}}} where i = imaginery square root of unity i.e. {{{i=sqrt(-1)}}}.



{{{(-25)^(-3/2)}}}
= {{{((5i)^2)^(-3/2)}}}
= {{{(1/(5i)^2)^(3/2)}}}
= {{{1/(sqrt((5i)^2))^3}}}
= {{{1/(5i)^3}}}
= {{{1/(125*i^3)}}}
= {{{-1/(125i)}}}
= {{{i^2/(125i)}}}
= {{{i/125}}}