Question 29083
Find:
{{{(-125)^(1/3)}}} So you are really looking for a number n, such that{{{n^3 = -125}}}
You try can factoring -125. But you want the factors to be identical, so start with +125.
You know 125 divides by 5 because its one's position is 5, so:
5(25) = 125 Now factor the 25 to get 5*5.
So, now you have 5*5*5 = 125 A good start, but you really want to get -125, try (-5)(-5)(-5) = -125 Aha! So:
{{{(-125)^(1/3) = ((-5)(-5)(-5))^(1/3)}}} = {{{((-5)^3)^(1/3)}}} = -5

The third root of -125 = -5