Do all rational exponents have whole number base integer derived from the fraction?
$a^b=c$ where $a$ and $c$ are whole numbers and $b$ is fraction
example: $b= 5/4$
How do I get $a$ that gives first whole $c$, please?
Thank you in advance for answer I should have known.
For $a^{p/q}$ to be an integer, assuming $p/q$ irreducible, $a^{1/q}$ must itself be an integer.
The smallest $a^{1/q}$ being $2$, the answer is
$$a=2^q.$$
For $b=\dfrac54$, $a=16$ and $c=32$.