Re: are rational exponents defined for negative bases?


LookSkywalker@xxxxxxxxx wrote:
> Kenneth Bull wrote:
> > Are rational exponents defined for negative bases?
> >
> > I couldn't see how, because if the denominator of the rational exponent
> > was an even number, we would be in trouble...
> >
> > let x < 0, m,n > 0, n be even :
> >
> > x ^ (m/n) = (nth root of x) ^ m
> > ^^^^^^^^^^^^^^
> > impossible
> >
>
> do it the other way....
>
> x ^ (m/n) = nth root ( x ^ m )
>
> using this, negative bases can be defined

Not if x < 0, m is odd, and n is even; you're still taking an even root
of a negative number.

--- Christopher Heckman

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