SOLUTION: Simplify. -125 to the -3/2 power

Question 41723: Simplify.
-125 to the -3/2 power
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Okay, we can express -125 as (-5)^3, so we have
(-125)^(-3/2) =
((-5)^3)^(-3/2) =
(-5)^(-9/2) =
1 / (-5)^(9/2) =
1 / [(-5)^4 * (-5)^(1/2)] =
1 / 625i*sqrt(5)
Now we have to rationalize by multiplying top and bottom by -i*sqrt(5) and we get
-i*sqrt(5) / 3125
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