−3²: is it 9 or −9?
It is −9. By the standard convention the exponent applies to the 3 alone, and the minus sign is applied afterwards. If you want the square of negative three, write (−3)², which is 9.
See it worked out
Standard convention
The exponent goes first, then the minus sign.
= −9
Written out: −(32)
With brackets: (−3)²
The bracket makes −3 one number, and that gets squared.
= 9
Written out: (−3)2
Think of the minus as −1 ×
A minus sign in front of a term acts like multiplying by −1, and multiplication comes after exponents. So −3² means −1 × 3² = −1 × 9 = −9.
Brackets change what is being squared
In (−3)², the bracket turns −3 into a single number, and squaring it gives (−3) × (−3) = 9. Same digits, different meaning.
Why calculators and spreadsheets disagree
Different tools handle a leading minus differently. Python evaluates -3**2 as −9, following the mathematical convention. Excel evaluates =-3^2 as 9, because it applies the negation before the exponent. A scientific calculator may give either, depending on the model. When in doubt, add brackets.
Why it matters in algebra
The graph of y = −x² is a parabola that opens downward, because x is squared first and then negated. The graph of y = (−x)² is the same as y = x², which opens upward. Mixing them up flips the whole picture.
Answers people give
| Answer | How you get there |
|---|---|
| −9 | −3²: exponent first, then the minus sign. |
| 9 | (−3)²: the bracket squares the negative number itself. |
| −6 | Treating the exponent as multiplication: −3 × 2. Wrong under any convention. |
Try your own expression
Type anything, including brackets, fractions and exponents, and get the steps.
Questions
Is −3² equal to 9?
Not by the standard convention. −3² is −9 because the exponent applies only to the 3. (−3)² is 9.
Why does my spreadsheet show 9?
Some spreadsheet programs, Excel among them, apply a leading minus sign before the exponent, so =-3^2 returns 9. Write =-(3^2) or use brackets to control it.