Finding the Equation for average cost. Calculus
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Does "C(x)" stand for "the cost C of x units"? If so, are you given an interval (of time or something) over which you are finding the average? Or are you finding the average cost of x units, in terms of the number of units? If the latter, then try using some actual numbers, and then noting how you operate with them.
For instance, if you have ten units that cost, in total, twenty bucks, what is the average cost per unit? What mathematical operation did you use to do that computation? What formula does this suggest?
I agree with stapel that the variables are not clearly defined. But looking again at exactly what you said, it appears that x = number of units, and
......Total cost of x units = 2^x
If that is true, then the average is found as you say, by dividing by x:
......Average cost per unit = (2^x)/x
There is no way to simplify that.
Is this from a calculus course or an economics course? if it is a question from a calculus course, it is very poorly specified.
If it is from an economics course, it is assumed that x is the number of physical units produced, x > 0, C(x) is total cost, and average cost
is C(x) / x.
So, in this case, average cost is simply \(\displaystyle \dfrac{C(x)}{x} = \dfrac{2^x}{x}.\)
This is, however, a very odd looking cost function. Are you sure you have specified it correctly?