What's the restriction (for $a, p, q$) when I use the following in proof?
$a^{p/q}=(a^{1/q})^{p}$
The calculus book give a list said:
$a$ $real$, $q$ $odd$ --------------- $a^{1/q}$, called the $q$th root of $a$, is the number $b$ such that $b^{q}=a$
$a$ $nonnegative$, $q$ $even$ ---- $a^{1/q}$ is the nonnegative number $b$ such that $b^{q}=a$
$rational$ $exponents$ -------- $a^{p/q}=(a^{1/q})^{p}$
I'm mess up by these restrictions.