a book says the "$6$th root of $(-8)^2$" is undefined "because the sixth root of '$-8$' is undefined"
is this a mistake?
$\color{#09476C}{\text{STUDY TIP}}$
Rational exponents can be tricky, and you must remember that the expression $b^{m/n}$ is not defined unless $\sqrt[n]{b}$ is a real number. This restriction produces some unusual-looking results. For instance, the number $\left(-8\right)^{1/3}$ is defined because $\sqrt[3]{-8}=-2$, but the number $\left(-8\right)^{2/6}$ is undefined because $\sqrt[6]{-8}$ is not a real number.
if we cancel exponents we get $$\sqrt[6]{(-8)^2}=\sqrt[3]{(-8)}=-2$$ and $$\sqrt[6]{(-8)^2}=\sqrt[6]{64}=2$$ two distinct values so it is not well defined