1Cademy - $$(-a)^n$$ Versus $$-a^n$$

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Exponential Notation in Algebra

Comparison

$(-a)^n$ Versus $-a^n$

When a negative sign appears alongside an exponent, the placement of parentheses determines what the exponent acts on, and this distinction can change the sign of the result:

$(-a)^n$ — The parentheses make the entire quantity $-a$ the base. The exponent directs you to multiply $-a$ by itself $n$ times. When $n$ is even, the product of an even number of negative factors is positive; when $n$ is odd, the product is negative.
$-a^n$ — Without parentheses enclosing the negative sign, only $a$ is the base. The order of operations requires the exponent to be evaluated first, producing $a^n$ , and then the negative sign is applied: $-a^n = -(a^n)$ . Because this is simply the opposite of a positive power, the result is always negative (when $a > 0$ ).

The critical takeaway is that parentheses around the negative sign cause the exponent to repeatedly multiply the negative number, whereas the absence of parentheses means the exponent applies only to the positive number and the negation happens afterward.

Updated 2026-04-21

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