SOLUTION: Kindly help me solving it If {{{a^b=b^a}}} then the value of {{{(a/b)^(a/b)-a^(a/b-1)}}} reduces to?

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Question 1045307: Kindly help me solving it
If a%5Eb=b%5Ea then the value of %28a%2Fb%29%5E%28a%2Fb%29-a%5E%28a%2Fb-1%29 reduces to?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I could begin with ,
but that gets rendered in a way that is hard to read,
so I will write the the same expression in a way that it can be read: %28a%2Fb%29%5E%28a%2Fb%29-a%5E%28a%2Fb-1%29%22=%22a%5E%22a%2Fb%22%2Fb%5E%22a%2Fb%22-a%5E%28%22a%2Fb%22-1%29
From the "If a%5Eb=b%5Ea " statement, we get
a%5Eb=b%5Ea ---> %28a%5Eb%29%5E%281%2Fb%29=%28b%5Ea%29%5E%281%2Fb%29 ---> a%5E%22b%2Fb%22=b%5E%22a%2Fb%22 --->a=b%5E%22a%2Fb%22 = the denominator in the expression above.
With that,
%28a%2Fb%29%5E%28a%2Fb%29-a%5E%28a%2Fb-1%29%22=%22a%5E%22a%2Fb%22%2Fb%5E%22a%2Fb%22-a%5E%28%22a%2Fb%22-1%29%22=%22a%5E%22a%2Fb%22%2Fa-a%5E%28%22a%2Fb%22-1%29%22=%22a%5E%28%22a%2Fb%22-1%29-a%5E%28%22a%2Fb%22-1%29%22=%22highlight%280%29