power - Maple Help

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combine/power

combine terms with powers

 Calling Sequence combine(f, power, symbolic)

Parameters

 f - any expression symbolic - (optional) literal name; allow formal symbolic manipulation of expressions

Description

 • Expressions involving powers are combined by applying the following transformations:

${x}^{y}{x}^{z}\mathbf{⇒}{x}^{y+z}$

${\left({x}^{y}\right)}^{z}\mathbf{⇒}{x}^{yz}$

${ⅇ}^{x}{ⅇ}^{y}\mathbf{⇒}{ⅇ}^{x+y}$

${{ⅇ}^{x}}^{y}\mathbf{⇒}{ⅇ}^{xy}$

$\sqrt{-a}\mathbf{⇒}I\sqrt{a}$

${a}^{n}{b}^{n}\mathbf{⇒}{\left(ab\right)}^{n}$

 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.

Examples

 > $\mathrm{combine}\left({x}^{3}{x}^{m-3},\mathrm{power}\right)$
 ${{x}}^{{m}}$ (1)
 > $\mathrm{combine}\left({\left({3}^{n}\right)}^{m}{3}^{n},\mathrm{power}\right)$
 ${\left({{3}}^{{n}}\right)}^{{m}}{}{{3}}^{{n}}$ (2)
 > $\mathrm{assume}\left(m,\mathrm{integer}\right)$
 > $\mathrm{combine}\left({\left({3}^{n}\right)}^{m}{3}^{n},\mathrm{power}\right)$
 ${{3}}^{{n}{}{\mathrm{m~}}{+}{n}}$ (3)
 > $\mathrm{combine}\left({\left(\mathrm{exp}\left(x\right)\right)}^{7}\mathrm{exp}\left(y\right),\mathrm{power}\right)$
 ${{ⅇ}}^{{7}{}{x}{+}{y}}$ (4)
 > $\mathrm{combine}\left({2}^{\frac{1}{2}}{3}^{\frac{1}{2}},\mathrm{power}\right)$
 $\sqrt{{6}}$ (5)
 > ${\left(-4\right)}^{\frac{1}{2}}$
 $\sqrt{{-4}}$ (6)
 > $\mathrm{combine}\left({\left(-4\right)}^{\frac{1}{2}},\mathrm{power}\right)$
 ${I}{}\sqrt{{4}}$ (7)
 > $\mathrm{combine}\left({\left(-2\right)}^{\frac{1}{2}}{3}^{\frac{1}{2}},\mathrm{power}\right)$
 ${I}{}\sqrt{{6}}$ (8)

 See Also