Write an exponential function whose graph passes through the given points (2,8) (5,512)

We are going to use the basic form of an exponential function:  to solve this problem.
Since we have tow points  and , we are going to have a system of equations:
equation (1)
equation (2) 

We know for our problem that , , , and , so lets replace those values in our equations: 
equation (1)
equation (2)

Now, we just need to find  and :

Dividing equation (2) by equation (1):



equation (3)

Replacing equation (3) in equation (1):





Finally, we can put our function together:



We can conclude that the exponential function whose graph passes through the points (2,8) and (5,512) is .