Where is the problem here:$-1=(-1)^1=(-1)^\frac{2}{2}=({(-1)}^{2})^{1/2}=\sqrt{1}=1$?

Question

Is there someone show me Why this is not true ?

$$-1=(-1)^1=(-1)^\frac{2}{2}=({(-1)}^{2})^{1/2}=\sqrt{1}=1$$

then :$$-1=1$$

Thank you for any help

Answer 1

You are not allowed to split indices like that if you have a negative number. $x=a^{bc} \not \implies x=(a^b)^c $ if a is negative. So the step $(-1)^1=((-1)^2)^{(1/2)}$ is wrong.