MHB Is this wrong or right? Simplify: -2^2 =-4

[OMGMathPLS]

Because on the test the answer given back says the correct answer for -2^2 is -4. Is there a difference between simplifying and solving?

 

[Dethrone]

In this case, there is no difference between simplifying and solving. And the answer of your question depends on whether you mean $-2^2$ or $(-2)^2$. I'm sure you are referring to the former, $-2^2$, in which the answer is $-4$. :D

 

[OMGMathPLS]

But... how? Why is it not (-2)(-2)= +4

 

[Jameson]

Hi OMGMathPLS,

Welcome to MHB! :)

As Rido12 wrote, this is technically correct. When evaluating $-2^2$ (no parentheses) you should square the "2" before you apply the negative. Think of it as $(-1)2^2$. This is kind of pedantic in my opinion with no context since potentially misleading notation is not good to use in practice, but it's important to always remember the order of operations.

 

[OMGMathPLS]

Ok, thanks Jameson.

 

[ineedhelpnow]

when you do $(-2)^2$ that is equal to (-2)(-2) which is 4. when you do $-2^2$ that is equal to -(2)(2) which is -4. make sense?

Simplifying: bringing it down to the lowest and most basic form
Solving: finding a final answer

 

[Ackbach]

How I teach my students is this: exponents "see" or "apply to" only the first thing down and to their left. If it's a parenthesis, then it'll apply to everything between that parenthesis and its matching parenthesis. Otherwise, it only applies to one symbol. The kind of expression for which $3^3-6^2$ is an example, is unambiguous and quite common; this particular expression's value is $3^3-6^2=27-36=-9$.