Common exponent rules question

[Gregory Cole]

On page 70 of NP, they list common exponent errors. It states -4 to the second power cannot be simplified, but (-4) to the second power =16. Can anyone explain the difference? Thanks!

[george.kourdin]

i am not sure whats going on here..what you wrote makes sense. perhaps post the exact explanation from the book?

[Gregory Cole]

Thanks for your help George. The book says -x to the 2nd power cannot be simplified. And the numerical example says that -4 to the second power = 16 is incorrect, but (-4) to the second power = 16 is correct. So my question is why is it correct when the -4 is inside parentheses as opposed to not.

Thanks again!

[george.kourdin]

taking any negative number to an even positive power gets rid of the negative sign so when they are referring to the squaring negative unknowns, they are probably referring to the fact that an even exponent masks the sign

i suppose the -4^2 =16 example is intended to display that..if not i am not sure. sorry man

[jnelson0612]

On page 70 of NP, they list common exponent errors. It states -4 to the second power cannot be simplified, but (-4) to the second power =16. Can anyone explain the difference? Thanks!

This is tricky! Remember PEMDAS, order of operations. Apply exponents BEFORE multiplying. Here's the difference:

-4^2: we first square the 4, which gives us 16, then we apply the negative sign (this is like multiplying by a negative 1) and receive -16.

(-4)^2: we apply the exponent and take -4 * -4 which is 16.

Hope this makes sense!

[JohnHarris]

On page 70 of NP, they list common exponent errors. It states -4 to the second power cannot be simplified, but (-4) to the second power =16. Can anyone explain the difference? Thanks!

Perhaps what they mean is that if you have (-4)^2 you can not drop the parenthesis' because you would get the wrong answer [but, if you have (+4)^2, you can drop the parenthesis']

[tim]

Thanks John..