Recall that one of the rules of exponents states that
[tex]x^{ \frac{m}{n} }= \left(\sqrt[n]{x} \right)^m[/tex]
Now, let x be a negative number and n, an even number, then
[tex](-x)^{ \frac{m}{n} }= \left(\sqrt[n]{(-x)} \right)^m[/tex]
But the even root of a negative number is not a real number.
for example, [tex] \sqrt{-1} [/tex] is not a real number, rather a complex number.
Hence, rational exponents are not defined when the denominator of the exponent in lowest terms is even and the base is negative.
