if (-2)^2 = 4 but -2^2 = -4 why are they different

think about this

 

$$20-3^2=20-9=11\\
so\\
-3^2 $ really means $ -1*3^2 = -9$$

A negative multiplied by a negative results in a positive number, therefore -2^2 (or -2 * -2) is 4. 

 

The calculator needs it to be wrapped in parantheses so it knows to square the negative number. Without parantheses, it calculates it like this:

 

-1*2^2

-1*4

-4