Thread: Maths dispute - a very simple simple exponents question

1. Maths dispute - a very simple simple exponents question

I had an indices test and I got the results back today (I didn't too shabby).

There was one question though that concerned me.

It is this one:

$\displaystyle -3^2$

It looks EXACTLY like this. No brackets or anything. Just $\displaystyle -3^2$

I wrote $\displaystyle -9$ and my teacher marked it wrong. I have asked my friends and they are all divded

My teacher said it was 9 but I thought i was only 9 when it was $\displaystyle (-3)^2$

Who is right?!? :S

2. Originally Posted by jgv115
I had an indices test and I got the results back today (I didn't too shabby).

There was one question though that concerned me.

It is this one:

$\displaystyle -3^2$

It looks EXACTLY like this. No brackets or anything. Just $\displaystyle -3^2$

I wrote $\displaystyle -9$ and my teacher marked it wrong. I have asked my friends and they are all divded

My teacher said it was 9 but I thought i was only 9 when it was $\displaystyle (-3)^2$

Who is right?!? :S

It is my opinion that almost any mathematician, even beginners, will agree that $\displaystyle -3^2=-9$ as the power does not apply on the minus sign (or, if you prefer, on -1) but only on the immediate expression it is upon.

Now, it could be that your teacher considers $\displaystyle -3$ as asingle expression (which, in fact, it is: the additive inverse of $\displaystyle 3$), but then we have a problem: how could we express the mathematical expression "the additive inverse of (3 raised to the second power)"??
Should we write the minus sign further away from 3: $\displaystyle -\,\,\,3^2=-9$ ?

These are question I'd ask, very respectfully, my teacher if I were you.

In general, I'd say you're right.

Tonio

3. -3^2 = 9
Whenever you square a number no matter if its positive or negative the outcome will always be positive. Do it on your calculator. -3*-3 = 9 if it were to be -3*3 then yes it would equal -9. but then the problem wouldn't be -3^2. Just remember whenever you see anything squared the answer will be positive.

4. -3^2 = -9 ; really means -(3^2)
(-3)^2 = 9

That's it, that's all. Roger.

5. As most have said, $\displaystyle -3^2$ by convention is $\displaystyle -9$. But it depends on what convention one decides to use for the “order of operations”. Usually, operations within an expression are evaluated in the following order:

1. Parentheses (brackets)
2. Powers (indices, roots)
3. Multiplication (or division)
The unary minus (additive inverse) follows the rule for multiplication by $\displaystyle -1$, so it is evaluated after the power has already been evaluated. Some, however, treat the unary minus as an operator whose order of evaluation follows parentheses yet precedes powers. I guess the only way to be sure is to ask your teacher which convention he or she follows.