Expressions involving powers are combined by applying the following transformations:

for arbitrary $x$, $y$, $z$, integers  $a,b>1$ , and rational $n$, when those transformations are valid.

If you specify the symbolic option, Maple performs formal symbolic manipulation of the expression f without regard to the analytical issue of branches for multi-valued functions.

Note: The sqrt command automatically applies a set of simplifications and normalizations that are not applied automatically by ^(1/2), thus the latter requires the use of combine.

$\mathrm{combine}\left(x^3{x}^{m-3}\,\mathrm{power}\right)$

$x^m$

$\mathrm{combine}\left({\left(3^n\right)}^m{3}^n\,\mathrm{power}\right)$

${\left(3^n\right)}^m{3}^n$

$\mathrm{assume}\left(m\,\mathrm{integer}\right)$

$\mathrm{combine}\left({\left(3^n\right)}^m{3}^n\,\mathrm{power}\right)$

$3^{n\mathrm{m~}+n}$

$\mathrm{combine}\left({\left(\exp \left(x\right)\right)}^7\exp \left(y\right)\,\mathrm{power}\right)$

${\ⅇ}^{7x+y}$

$\mathrm{combine}\left(2^{\frac{1}{2}}{3}^{\frac{1}{2}}\,\mathrm{power}\right)$

$\sqrt{6}$

${\left(-4\right)}^{\frac{1}{2}}$

$\sqrt{\mathrm{-4}}$

$\mathrm{combine}\left({\left(-4\right)}^{\frac{1}{2}}\,\mathrm{power}\right)$

$\mathrm{I}\sqrt{4}$

$\mathrm{combine}\left({\left(-2\right)}^{\frac{1}{2}}{3}^{\frac{1}{2}}\,\mathrm{power}\right)$

$\mathrm{I}\sqrt{6}$