Can I Separate a Constant and Variable Expression in Exponential Manipulation?

[winterwind]

Homework Statement

I am working on a problem, and there is a small step I need help on:

I have the expression e^ab, where a is a constant, and b is a variable. I need to separate a and b so I can pull out the expression b from an integral expression. Is there any exponent law or manipulation I can do algebraically that will allow me to get separate the constant a expression from the variable b expression?

Homework Equations

Rules of exponents, algebraic manipulations.

The Attempt at a Solution

There isn't any simple rule (i.e. x^mxⁿ = x^m+n) that I can use to separate the two expression. I've tried moving the expression around, to no avail. Any help is appreciated!

 

[rock.freak667]

The Attempt at a Solution

(i.e. x^mxⁿ = x^m+n) !

Why can't you use that? What is the integral expression you are talking about?

 

[winterwind]

Why can't you use that? What is the integral expression you are talking about?

Unfortunately, that doesn't work, since the expression is e^ab. I would only be able to use that rule if it were e^ae^b. The constant a is multiplied to the variable b in the same exponential.

The integral expression is: v³/[e^v(h/kT) -1] where v is the variable, and (h/kT) is constant. Essentially, I need to get the expression in the form x³/(e^x-1) , where then I can use a table of integrals to evaluate the integral. Is there a simple way to get the above expression into that form? In this case, v = x, so I am close, but there is the (h/kT) constant term in the exponential that still needs to be taken care of.

 

[vela]

You're overthinking it. Use the substitution $x=\nu(h/kT)$.

 

[Bohrok]

e^ab = (e^a)^b and e^a is just a constant.

Then ∫b^x dx = b^x/ln(b) + C

 

[winterwind]

You're overthinking it. Use the substitution $x=\nu(h/kT)$.

Thanks! This is it.