If $n$ is a positive integer and $n=r^e$, where $r$ and $e$ are positive integers with $1<e$, then iperfpow( n ) returns r. If the second argument, p, is specified in the calling sequence, then it is assigned the value e.

It is an error for n to evaluate to a numeric which is not a positive integer.

This command returns FAIL if it is not able to establish that n is a perfect power of an integer.

In all other cases, the command returns unevaluated.

$\mathrm{iperfpow}\left(256\right)$

$16$

$\mathrm{iperfpow}\left(125\&comma;'p'\right)$

$5$

$p$

$3$

$\mathrm{iperfpow}\left(216\&comma;'p'\right)$

$6$

$p$

$3$

$\mathrm{iperfpow}\left(12\right)$

$\mathrm{FAIL}$

$\mathrm{ifactor}\left(12\right)$

${\left(2\right)}^2\left(3\right)$

$\mathrm{iperfpow}\left(1\&comma;'p'\right)$

$1$

$p$

$2$

$\mathrm{iperfpow}\left(x\right)$

$\mathrm{iperfpow}\left(x\right)$

$\mathrm{iperfpow}\left(-25\right)$

Error, (in iperfpow) first argument must be a positive integer