As I moved through algebra, I was taught that fractional exponents could be evaluated in one of two ways:
$$ x^\frac{a}{b} = (\sqrt[b]{x})^a = (\sqrt[b]x^a)$$
However, suppose $x=-2$ and $a=6$ and $b=4$:
If we evaluate using the first expression, we get:
$$(\sqrt[6]{-1})^4 = DNE$$
This is because we cannot take the even root of a negative number.
But, if we evaluate using the second expression, we get: $$(\sqrt[6]x^4) = 1$$
Any explanation on what is going on? Thanks!
