# Maths dispute - a very simple simple exponents question

• May 4th 2010, 01:03 AM
jgv115
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
• May 4th 2010, 01:59 AM
tonio
Quote:

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
• May 4th 2010, 08:07 AM
TheJosephOuellette
-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.
• May 4th 2010, 08:16 AM
Wilmer
-3^2 = -9 ; really means -(3^2)
(-3)^2 = 9

That's it, that's all. Roger.
• May 4th 2010, 09:08 AM
Tikoloshe
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)