# exponentiation

• May 9th 2013, 04:19 PM
LChenier
exponentiation
We have to compute this .. on a computer
Attachment 28311
seems very easy, but me and my partner cant agree on something
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I say that this is to be see as

X = bm/n

b being negative and n being even, the answer is the complex number 5i
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my partner says:

this should be see as

X = (bm)1/n

giving the answer 5 and -5
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I say that he is wrong because:
if I reverse the function,

((-5)4)1/2 = 25, not -25
((-5)1/2)4 = 25, not -25

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and

((5i)1/2)4 = -25
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but he wont see this as a proof since the programs "Maple" and also "Microsoft Math" does return 5 and -5
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Please, tell me who is right ??
• May 9th 2013, 05:11 PM
Plato
Re: exponentiation
Quote:

Originally Posted by LChenier
We have to compute this .. on a computer
Attachment 28311

Oh come on! Anyone with very very basic algebra skills knows that:

$\sqrt[4]{{{x^2}}} = \sqrt {\left| x \right|}$.

If that leaves you (or anyone) clueless, please consult any middle-school mathematics teacher.
• May 9th 2013, 06:53 PM
LChenier
Re: exponentiation
I know that, but:

sqtr(|-25|) = 5

then why

5^2 <> -25
(5^(1/2))^4 <> -25

why

the 4th root of -5 is sqrt(5i) and sqrt(5i)^2 = 5i

where now,

(5i^(1/2))^4 = -25