5.96 How to simplify \(e^{\ln (x)+\ln (y)}\)

given

\[ {\mathrm e}^{\frac {2 \ln \left (\sqrt {p^{2}+1}+p \right )+2 \ln \left (a \right )+\ln \left (p^{2}+1\right ) a}{2 a}}+{\mathrm e}^{3 x} \]

simplify(expr) does not work. So tried subsindets

restart; 
expr := exp((2*ln(sqrt(p^2 + 1) + p) + 2*ln(a) + ln(p^2 + 1)*a)/(2*a))+ exp(3*x); 
subsindets(expr,'specfunc( anything, exp )',f->(`if`(has(op(1,f),'ln'),expand(f),f)))
 

\[ \left (\sqrt {p^{2}+1}+p \right )^{\frac {1}{a}} a^{\frac {1}{a}} \sqrt {p^{2}+1}+{\mathrm e}^{3 x} \]

It is possible to also try simplify(expr,exp) in some cases, but for the above example, this did not work, i.e. it did not simplify it.

Update December 2023. Trying Maple 2023.2.1, it simplifies the above using simplify(expr,exp)

restart; 
expr := exp((2*ln(sqrt(p^2 + 1) + p) + 2*ln(a) + ln(p^2 + 1)*a)/(2*a))+ exp(3*x); 
simplify(expr,exp)
 

\[ sqrt{p^{2}+1}\, \left (\sqrt {p^{2}+1}+p \right )^{\frac {1}{a}} a^{\frac {1}{a}}+{\mathrm e}^{3 x} \]

And

restart; 
expr:=exp(ln(x)+ln(y)); 
simplify(expr)
 

\[ x y \]