Can someone please help!? I don't understand how to do this. ^16sqrt((-8)^16)

- anonymous

Can someone please help!? I don't understand how to do this. ^16sqrt((-8)^16)

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- anonymous

|dw:1332368433787:dw|

- Zarkon

\[\sqrt[16]{(-8)^{16}}=|-8|=8\]

- anonymous

the 16's cancel out

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## More answers

- anonymous

Ok so the 16's cancel out...which leave the sqrt(-8)

- anonymous

The negative sign in front of the eight disappears because power of 16 is even. So if you multiply -2X-2 you get 4 if you multiply -2X-2X-2 you get -8

- anonymous

ok so the answer is the sqrt(8)?

- Zarkon

I already gave you the answer...why don't people believe me :)

- anonymous

didn't say I didn't believe you just trying to understand it also.

- anonymous

|-8|=8\] so this is the answer you gave? correct?

- Zarkon

the answer is 8

- anonymous

The answer is 8. Just to clarify what happened,: -8^16=-281X10^12 then the 16th root of that result is 8

- anonymous

I would check with your textbook or teacher. I could see arguments made for both cases. Ultimately, I would call it\[\pm8\]
I've seen books that treat negative numbers under even rooted radicals as negative simply because the question was asked with a negative under the radical.
I would go with -8 if you have to pick one though.

- Zarkon

when the notation \[\sqrt[n]{}\] then the value wanted is the principal value otherwise there are 16 answers

- anonymous

Ok so your suggesting to go with the answer of -8? Once I put that answer in I can't go back and change it. It is an online quiz.

- anonymous

|dw:1332368998213:dw|

- anonymous

THANK YOU for drawing it out...that helped alot!

- anonymous

I would look for an example in your textbook before submitting the answer online.

- phi

bjc, Zarkon gave you the correct answer.
The problem is that there are subtleties with this question. There are 16 different answers. but unless you are expected to find all of them you give the principal root. That will be 8

- anonymous

As I said, I could see arguments going either way on this one.

- Zarkon

http://www.wolframalpha.com/input/?i=16th+root+of+%28-8%29^16

- anonymous

There we go!

- anonymous

Ok thanks so much everyone...I think this is the most responses on a question i have ever gotten. It helps!

- anonymous

I use wolfram but have never been able to figure out how to put in the 16th root...thanks for showing me how to do that too! LOL

- anonymous

Be careful...
http://www.wolframalpha.com/input/?i=%2816th+root+of+%28-8%29%29^16

- Zarkon

TheFigure: that is a different problem

- anonymous

I'm totally open to the idea that I'm wrong. This is a fuzzy area. :)

- anonymous

Well you guys have been completely helpful. Thanks again.

- anonymous

It was my understanding these were completely interchangable.
|dw:1332369436288:dw|
Oh, bjcjdj2020, which answer ended up working?

- anonymous

I won't know until after I finish my quiz but I used 8.

- anonymous

I have about 64 questions to go.

- anonymous

Good luck!

- anonymous

and I am open for any more help! LOL Its my final quiz and math isn't my area of expertise

- anonymous

TY

- anonymous

Well, good luck friend! I'd be curious to know how it turns out! :)

- anonymous

I will post to let you all know how the quiz goes.

- Zarkon

they are interchangable if \(x\ge 0\)

- Zarkon

for any positive even integer \(n\)
\[\sqrt[n]{x^n}=|x|\]

- phi

@TheFigure This only gives the rules, (near the bottom),
http://www.mathsisfun.com/numbers/nth-root.html
not much insight.

- anonymous

OK, so there is a little restriction I was unaware of. Thank you for bringing it to my attention. It'll make me better at this! :)

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