It's indeed . For example, consider which is offcourse and therefore there're not equal.
So it's important to use brackets!
However, brackets come before exponents so if the multiplication is done inside the bracket it too is affected by the exponents.
- the brackets here are unnecessary and only serve to complicate matters IMO.
The order of operands is very important, and this is where you're having trouble.
-9 is essentially like saying 0 - 9, you just omit the 0.
Now, from BIDMAS, we know that everything in brackets is evaluated first, and that indices/multiplication is evaluated before subtraction.
So (-9^2) is like saying (0 - 9^2). You evaluate the index first, then you subtract the result from 0.
0 - (9)(9) = 0 - 81 = -81
Whereas, in (-9)^2 you evaluate everything in brackets first, so (0 - 9)^2 = (-9)(-9) = 81, because multiplying an even number of negatives together results in a positive.
I hope that was clear enough.