Question 896086
<pre>
{{{matrix(2,1,"",a^(1/ln(a)))}}}

Let x equal to the expression:

{{{matrix(2,1,"",x)}}}{{{matrix(2,1,"",""="")}}}{{{matrix(2,1,"",a^(1/ln(a)))}}}

Take natural logarithms of both sides:

{{{matrix(2,1,"",ln(x))}}}{{{matrix(2,1,"",""="")}}}{{{matrix(2,1,"",ln(a^(1/ln(a))))}}}

Use the rule of logarithms {{{ln(P^Q)=Q*ln(P)}}}

{{{ln(x)}}}{{{""=""}}}{{{(1/ln(a))ln(a)}}}

{{{ln(x)}}}{{{""=""}}}{{{(1/cross(ln(a))[1])cross(ln(a))^1}}}

{{{ln(x)}}}{{{""=""}}}{{{1}}}

Use the fact that the natural log equation {{{ln(P)=Q}}} 
is equivalent to the exponential equation {{{e^Q=P}}}

{{{e^1}}}{{{""=""}}}{{{x}}}

{{{e}}}{{{""=""}}}{{{x}}}

Answer: it simplifies to e.

Edwin</pre>