Answer:
Rational exponents are not defined when the denominator of the exponent in lowest terms is even and the base is negative.
Step-by-step explanation:
Considering the expression
[tex]X^{\frac{a}{b}}=\sqrt[b]{X^a};\:\:\:\:\:\:\:\:\:b\ne 0[/tex]
Here:
A rational exponent - an exponent that is a fraction - is the kind of way we may write a root.
If the denominator is an even number, it means we are talking about an even root like square root, 4th root, 6th root etc.
For example, think about squaring a number
-4 × -4 = 16, 4 × 4 = 16
It means any number when it get multiplied by itself an even number of times, it would always yield a positive number.
It is not possible to take the square root of a negative number as we can not yield a negative number when we square the number. In other words, there is no way we can multiply the same negative number twice and get a negative number. This is why [tex]\sqrt{-1}[/tex] is undefined.
Therefore, rational exponents are not defined when the denominator of the exponent in lowest terms is even and the base is negative.
