What is the value of b?

To determine the value of ( b ) in the exponential function ( f(x) = b^x ), we can use the given points.

1. From the point ( (2, 16) ):

[

f(2) = b^2 = 16

]

This implies:

[

b^2 = 16 implies b = 4 quad (text{since } b text{ must be positive})

]

2. Let’s check this value with the other points:

– For ( (3, 64) ):

[

f(3) = b^3 = 4^3 = 64 quad text{(Correct)}

]

– For ( (4, 256) ):

[

f(4) = b^4 = 4^4 = 256 quad text{(Correct)}

]

Since the calculations are consistent, the value of ( b ) is:

[

boxed{4}

]