Re: are rational exponents defined for negative bases?


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

This topic even confuses scientific calculators...

Most that I've seen will correctly calculate an odd root of a negative
number... For example, the 5th root of -32 results in -2. They will do
this even if you enter it as (-32)^(1/5) or even (-32)^(2/10) or
(-32)^(2.2/11) or (-32)^(0.2)

But they give an error message if the exponent becomes a fraction with
an odd denominator and a numerator other than 1.

For example, (-32)^(2/5) doesn't work...

.

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