involves an nth root, so it may be
positive, negative, or undefined.
Example. You can use a calculator to
compute roots and powers. How you do this depends on what kind of
calculator you have. For example,
Roots of negative numbers can present a problem; some calculators will
return a complex number , or
give an error message. You can fix things by figuring out the sign of
the result beforehand. Then make the
base positive for your calculator and fix the sign at the end.
For example, is an odd root of a
negative number, so it’s negative. Knowing this, I use the
calculator to compute
Example. There is some ambiguity here. For
But should be undefined, since
I’m taking an even root of a negative number. I will avoid this
problem by always expressing fractional exponents inlowest terms .
The rules I gave earlier for working with integer
exponents work with fractional exponents — with
certain exceptions for even roots.
is not the same as x.
is always nonnegative. But x could
be negative: For example,
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