Powers in Expressions

Evaluate n^2 + 4n when n is -5. Substitute in parentheses everywhere n appears: v = (-5)^2 + 4 × (-5). Powers come first: (-5)^2 is -5 times -5, which is 25. Then 4 times -5 is -20, so the line becomes v = 25 - 20, and v = 5.

Here the parentheses decide the answer. (-5)^2 squares the whole number -5 and gives 25. But -5^2 means the opposite of 5^2: the power belongs to the 5 alone, so it is -25. Leave out the parentheses and you square the wrong thing.

That is why a squared negative input always comes out positive: a negative times a negative is positive. If your value for n^2 is negative, a pair of parentheses went missing.