It is not obvious to me how the file data relates to the expression. I assume this was discussed in class, or in other parts of the assignment.
This is a nonlinear parameter estimation problem. One relatively straightforward way to solve it is to take the logarithms of both sides, then solve it as a linear equation, using polyfit and polyval. (The best way is to use nonlinear parameter estimation techniques, however linearizing it will likely provide useful results if the noise is relatively low.)