Where the Minus Lives

(-5)^2 and -5^2 look alike, but they are different. In (-5)^2, the parentheses put the minus sign inside the base, so both factors are negative: (-5)(-5) = 25. In -5^2 there are no parentheses. The exponent is applied before the minus sign, so -5^2 means the opposite of 5^2, which is -25.

An exponent applies to its base. Parentheses make the whole expression inside them the base. Without parentheses, -5^2 means -(5^2) = -25. With parentheses, (-5)^2 = 25.

When you want to square a negative number, write it in parentheses. When you read an expression without parentheses, apply the exponent first and the minus sign after it.