Why does -4^2 equal -16 and not +16?

Thank you Heureka and thankyou anons for voicing your concerns.   

If you want to learn effectively you MUST speak up.    

This is always a source of confusion.   

Firstly

$$\\-4^2=-1*4^2=-1*16=-16\\
$Where as $\\
(-4)^2=-4*-4=+16\\\\
$Now why is this so?$\\
consider\\
50-3^2=50-9=41\\
$ See how the minus sign DID NOT belong to the 3$\\
$If it did belong to the 3 then this would be how it had to be done$\\\\
50+(-3)^2=50+9=59 = 50+3^2\\\\$$

Now I do not think that anyone would think    $$50+3^2$$     should equal   $$50-3^2$$

so the minus sign cannot belong to the 3       

Why does -4^2 equal -16 and not +16 ?

$$-4^2 = (-1)[(4)^2]=(-1)[16]=-16\\\\
(-4)^2 = [(-1)*(4)^2]=(-1)^2*(4)^2=1*16=16\\$$

by the way -4^2 does = 16, not -16 because -4*-4=16. 2 negatives make a positive, duhhhh!!!! dont hit the minus, hit the negative

if it was -(4^2)=-16 it would be right but -4^2=16