TITLE: Why is $-5^2=-25$?
QUESTION [5 upvotes]: If $-5^2$ is equal to $(-5)(-5)$, doesn't that mean the negatives should cancel each other out and become $25$? Why is this not the case?

REPLY [2 votes]: Because you forgot the parentheses. You meant to calculate $(-5)^2$ but instead calculated $-(5^2)$. When in doubt, use more parentheses than seem necessary.

By the way, this also applies to imaginary numbers: $(-5i)^2 = -25$, but $-(5i)^2 = 25$.
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