evaluate : (-25) to the 3/2 power

Question

Please can someone tell me why my calculator says "domain error" when I put this problem in it?

Answer 1

Your problem is trying to take the square root of a negative number.

Note that i=√(-1) and i² = -1

 

(-25)^3/2 = [(-25)^1/2]³ = (5i)³ = 625i³ = -625i

 

There are no real numbers that fit this expression