How do you find the value of an exponential function

We have

96 = ab⁵        and  384 = ab⁷    Using the first, we have 96/b⁵  = a

Substituting into the second, we have

384 = (96/b⁵ ) b⁷    simplifying, we have

384 = 96b²      divide both sides by 96

384/96 =  b²

4 = b²

2 = b     and using  ..... 96/b⁵  = a     ... we have     96/(2)⁵ = a    96/32 = a  = 3

So....our function is .... f(x) =  3(2^x)