Why doesn't  -(9) to the third power equal (-9) to the 3rd power? Isn't the answer to both Negative 729?

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.

by Top Rated User (614k points)