# math fallacy problem: $-1= (-1)^3 = (-1)^{6/2} = \sqrt{(-1)^6}= 1$?

I know there is something wrong with this but I don’t know where. It’s some kind of a math fallacy and it is driving me crazy. Here it is:
$$-1= (-1)^3 = (-1)^{6/2} = \sqrt{(-1)^6}= 1?$$

## Answer

The “rule” $(a^b)^c = a^{bc}$ doesn’t necessarily hold when $a < 0$.

Attribution
Source : Link , Question Author : newcomer , Answer Author : mrf