Exponent Math Question

Helping a kid with a math question. Question is -4^2. I thought the answer was 16 but the answer key states -16. I had thought the only was the answer could be -16 is if the question was specifically stated as -(4^2) or maybe -(4)^2?
Thoughts?

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the key is wrong, square roots of negatives are called imaginary numbers

Question isn't dealing with square ROOTS. Just dealing with a square.

The point is that (-4)^2/2 = -4

-4^2 = -16 then
-16^.5 = 4i, which is not -4

Order of operations
Exponentiation goes before negation.

[math](-4)^{2} = 16[/math]
[math]-(4)^{2} = -16[/math]

this
[math]-4^2=-(4^2)=-16[/math]
[math](-4)^2=16[/math]

(-4)^2/2 = 8
-4^2 = -16
(-4)^2 = 16
-16^.5 = -4
(-16)^.5 = 4i

You seriously need to learn math.

While I haven't done this kind of math in 20 years, I thought I remembered learning that -4^2 would be written as (-4)^2 as opposed to -(4)^2.
Anybody have any reputable sources to confirm what this notation should be written as?

Think of it like this (-4)^2=(-4)(-4) and -4^2=-(4*4)

I suppose my issue with the question is that when the parentheses aren't explicitly written, which assumption of where the parentheses should be included is correct? With the negative or without?

I understand this part of the question, but the original question didn't state specific parentheses.

in an actual expression there might be a squared 4 term being subracted from something else e.g.

[math] a - (4)^{2} = a - 16 [/math]

Context is key here.
This is the most succinct answer. If the question is actually -x, and x has a value of 4^2, then it would be -1 (4^2) as the value of x is multiplied by the implied negative one.

Don't assume parenthesis if they are not there. You only need them to to separate numbers for clarity, for multiplication, to group numbers together or to indicate the order of operations

A negative is always thought of as -1 times that number. So -4^2 = -1*4^2.

Now by order of operations we do the exponent, then multiplication.

Wrong.

-x is shorthand for (-x) by convention.

Show me a college text where this isn't assumed

-4^i = -16y ++;

this

yeah, the [math]4^{2}[/math] is a number in it's self, so the - sign before it is the negative of that number. so -16 would be correct.

Exponentiation goes before multiplication and - is short hand for -1*

so you should be considering -1*4^2 which evaluates to -16

bad answer key

I hope you're trolling

sorry, if you have something better to say, just say it

This exact example is explained here
khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/cc-7th-exponents-negative-base/v/exponents-with-negative-bases