The answer here has to do with order of operations rules (PEMDAS).
–2^4 comes out to -16, because the exponentiation MUST be done first. That gives you 16, which you then preface with the - symbol.
(–2)^4 Here the parentheses make the difference: (-2)^4 requires that we take the 4th power of (-1) and mult. that by the 4th power of 2, which is 16.
So, yes, –2^4 and (–2)^4 are different.
What about –2^3 and (–2)^3?
Again we must do exponentiation first. 2^3 is 8, which we then preface with -. Result: -8. (–2)^3 is equivalent to (1)^3 * 2^3, or (-1)*8, or -8. So these two results are identical.
Perhaps it would help to recall that
-1 = -1
(-1)^2 = 1
(-1)^3 = -1
(-4)^4 = 1
and that this pattern repeats itself after you've written each group of 4 lines.
and plug in the values for x and y.
