Evaluate $(-3)^2$, $3^2$ and $-3^2$. Evaluate each of the numeric expressions $(-3)^2$, $3^2$ and $-3^2$.
When I originally asked this problem I confused it with another problem...please help...thank you
 A: $3^2 = 3\cdot 3 = 9$
$(-3)^2 = (-3)\cdot (-3) = 9$
$-3^2 = -(3\cdot 3) = -9$
The crucial point is that in the expression $-3^2$, the minus sign is not included in the square (multiplication first).
A: [1]. $(-3)$ to the second power: $(-3)^2=(-3)\times(-3)=(-1)\times(3)\times(-1)\times(3)=9$.
[2]. $3$ to the second power: $(3)^2=(3)\times(3)=9$.
[3]. $-3^{2}=-(3)\times (3)=-9$.
Edit:
Deriah, here is a response to your comment, to clarify number [1].
First of all, things you should know:
A1. In general, if $m$ is a number, then $m^{2}=m\times m$, so, if we let $m=-1$, then $(-1)^{2}=(-1)\times (-1)$. If we let $m=-2$, then $(-2)^{2}=(-2)\times (-2)$. If we let $m=5$, then $5^{2}=5\times 5$, and so on.
A2. In general, if $z$ is a number with a minus sign, then we can take out $(-1)$ from $z$. For example, if we let $z=-1$, then we have $z=(-1)\times 1$. If we let $z=-2$, then we have $z=(-1)\times 2$. If we let $z=-3$, then we have $z=(-1)\times 3$, and so on.
A3. The order of multiplication doesn't matter. For example, $-3\times 1=1\times(-3)$, $(-1)\times 5=5 \times(-1)$, $3\times 7=7 \times3$ and so on.
A4. In general, if $m$ is a number, then $(-m)\times (-m)=m\times m$, so, if we let $m=1$, then $(-1)\times (-1)=1\times 1=1$, if we let $m=2$, then $(-2)\times (-2)=2\times 2=4$, if we let $m=3$, then $(-3)\times (-3)=3\times 3=9$, and so on.

Now, responding to you comment, in number [1] we have $(-3)$ to the second power:
First of all, we use A1, so we have $$(-3)^2=(-3)\times(-3),$$
Next, we use A2 to separate $(-1)$ from $3$, so we have
$$(-3)\times(-3)=(-1)\times(3)\times(-1)\times(3).$$
Then, we use A3 to rearrange the numbers and multiply them,
$$(-1)\times(3)\times(-1)\times(3)=(-1)\times(-1)\times(3)\times(3).$$
Next, we use A4 to multiply $(-1)\times(-1),$
$$(-1)\times(-1)\times(3)\times(3)=1\times 9.$$
And finally,
$$1 \times 9=9.$$
Alternatively, firstly using A1 and then A4, we can calculate it quicker,
$$(-3)^2=(-3)\times(-3)=9.$$
I hope this helps. Do tell me if you need more clarification.
