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Topic: math paradox
Replies: 7   Last Post: Jul 14, 2003 2:47 AM

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Wilbert Dijkhof

Posts: 201
Registered: 12/8/04
Re: math paradox
Posted: Jan 7, 1998 5:00 AM
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NATHANIEL SILVER wrote:

> > -1=(-1)^3=(-1)^(6/2)=sqrt((-1)^6)=sqrt(1)=1

> (-1)^(6/2)=sqrt((-1)^6) is not true.

Ok.

> When real number b < 0, then b^(m/n) = (b^m)^(1/n) and b^(m/n) =
> (b^(1/n))^(m) hold, if m/n is reduced to lowest terms.
>
> That's why calculators operations are defined (only when x >= 0) for
> (x^(1/n))^m, (x^m)^(1/n), and not for x^(m/n). The user takes it from there
> with the absolute value key (and split domains for functions).
>
> In a similar conundrum, (-8)^(1/3) is not equal to (-8)^(2/6).


I think they are equal. (If not, what's the difference according to you?)

> Dr. Dunce

Wilbert







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