What is the difference between squaring a negative number inside and outside of parentheses? [duplicate]
By Emma Valentine •
What is the difference between: $ -3^2 $ and $ (-3)^2 $ ? I know $-3^2 = -9$ and $(-3)^2 = 9$ but I don't know why.
$\endgroup$ 62 Answers
$\begingroup$It's a matter of the order of operations.
If you write $-3^{2}$, you're saying "the square of 3, now make it negative" = "9, now make it negative" = "-9".
If you write $(-3)^{2}$, you're saying "make 3 negative, now square it" = "-3, now square it" = "(-3)(-3)" = "9".
$\endgroup$ $\begingroup$So by convention, the power operation has higher priority than multiply operation unless you have "$()$" to indicate priority.
$$-3^2=-1\times 3^2=-1\times 3\times 3$$
While
$$(-3)^2=(-3)\times (-3)=(-1\times 3)\times (-1\times 3) = -1\times -1 \times 3\times 3$$
$\endgroup$
