Why does;
(-10)^2 = 100 but,
-10^2 = -100 ?

For (-10)^2 you are multiplying -10x-10, so basically the whole expression. the answer is 100. but for the other one, the exponent goes along with 10, and the negative sign gets put on after, so it's -100

Because  you did not use the ( ) When working with a negative number, it is always best to use brackets, this doesn't confuse the calculator.  In all equations is great ! it will always come out correct..