How do I get x^(e^(x-1)) from (x^e^x) divided by x?

By exponential property, x^(e^(x))/x can be written as...

x^(e^(x)) * x^(-1)

= x^(e^(x) - 1)

BUT you can't get x^(e^(x - 1)) since you are not multiplying exponents in this manner..

I hope this helps!

You don't because this is wrong.

If yoou let, for the time being, e^x=y, then

you have x^y/x=x^(y-1)=x^(e^x-1) and not x^(e^(x-1))=x^e^x/e.

The following site does a reasonable job of

explaining why exponents work the way they do.

http://oakroadsystems.com/math/expolaws.htm