Yes, -(9)³=(-9)³=-729, but -(9)² is not the same as (-9)², because -(9)²=-81 and (-9)²=81.
If we write -9=-1×9 then the reason becomes clear. (-1)³×(9)³ is the same as (-9)³.
(-1)³=-1 so (-9)³ is the same as -1×(9)³.
-1 to an odd power is -1, but -1 to an even power is 1. This is because of the rule about multiplying numbers with signs. Minus time minus is plus, so -1×-1×-1=-1, because any pair of -1’s multiplied together produce 1.
In -(9)², the parentheses show what action is to be done first, and this can also be written -(9²). The answer is -81 in each case. But if we put the minus inside the parentheses, then we have (-1)²(9)² which is the same as (-9)² and we have 1×81=81.
Parentheses only tell you what to do first and sometimes they can be omitted and you still get the same result. For example, (3)+(4) is the same as 3+4. But 2×(3+4) tells you to add 3 and 4 together then multiply the result by 2; but 2×3+4 tells you to multiply 2 and 3 then add 4 to the result. This could also be written (2×3)+4 without changing the result, because the parentheses are not necessary. PEMDAS tells you in what order you need to do a calculation: and P (parentheses) comes before everything else: work out the contents of the parentheses first, if you can, otherwise apply distributive laws, that is, apply what’s outside the parentheses to each term inside.