1Cademy - Simplifying $$(-7)^2$$ and $$-7^2$$

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Simplifying $(-2)^4$ and $-2^4$

Example

Simplifying $(-7)^2$ and $-7^2$

These two expressions further demonstrate how parentheses change the base and the resulting sign when raising a negative number to an even power:

ⓐ $(-7)^2 = 49$ : The base is $-7$ . The exponent tells us to multiply $-7$ by itself: $(-7)(-7) = 49$ . The product of two negative numbers is positive.

ⓑ $-7^2 = -49$ : The base is $7$ . The expression means "the opposite of $7^2$ ." First evaluate the power: $7^2 = 7 \cdot 7 = 49$ . Then apply the negative sign: $-49$ .

Like previous examples, the parentheses in part (a) ensure the negative sign is part of the repeatedly multiplied base, producing a positive result. Without parentheses in part (b), the exponent is evaluated first following the order of operations, and the result is then negated.

Updated 2026-04-20

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OpenStax Intermediate Algebra

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