Question 653238
Great question!  They're not!

(-4)^2 = (-4)(-4)
-4^2 = (-1)(4)(4)  <-- here, just the 4 is being squared.

In any negative number, there's a -1.  So, -4 is really (-1)(4).  Therefore, -4^2 is (-1)(4)(4).  PEMDAS says to exponents before multiply so we do 4^2 before multiplying by the -1 out front.