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combine/exp

combine exponentials

 Calling Sequence combine(f, exp)

Parameters

 f - any expression

Description

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

${ⅇ}^{x}{ⅇ}^{y}\to {ⅇ}^{x+y}$

${{ⅇ}^{x}}^{y}\to {ⅇ}^{xy}$

$\mathrm{exp}\left(x+n\mathrm{ln}\left(y\right)\right)\to {y}^{n}{ⅇ}^{x}\mathrm{where}n\mathrm{is}\mathrm{an}\mathrm{integer}$

Examples

 > $\mathrm{combine}\left({ⅇ}^{x}{ⅇ}^{-x},\mathrm{exp}\right)$
 ${1}$ (1)
 > $\mathrm{combine}\left({\left({ⅇ}^{5}\right)}^{2}{ⅇ}^{3},\mathrm{exp}\right)$
 ${{ⅇ}}^{{13}}$ (2)
 > $\mathrm{combine}\left({ⅇ}^{x+3\mathrm{ln}\left(y\right)},\mathrm{exp}\right)$
 ${{y}}^{{3}}{}{{ⅇ}}^{{x}}$ (3)
 > $\mathrm{combine}\left({ⅇ}^{x+\frac{3\mathrm{ln}\left(y\right)}{2}},\mathrm{exp}\right)$
 ${{ⅇ}}^{{x}{+}\frac{{3}}{{2}}{}{\mathrm{ln}}{}\left({y}\right)}$ (4)