Which equation below gives an incorrect value for the function k(x) = 512 x ?

a.) k(2/3)=64
b.) k(4/9)=16
c.) k(1/3)=8
d.) k(2/9)=8

The function is  k(x) = 512 · x .

Try 'A':      k(2/3) = (512) · (2/3) =  341.33...   not 64

Try 'B':      k(4/9) = (512) · (4/9) =  257.55...    not 16  

Try 'C':      k(1/3) = (512) · (1/3) =  170.66...    not 8

Try 'D':      k(2/9) = (512) (2/9) =  113.77...    not 8 .

So far, it looks like NONE of the choices is correct.

But wait !  There's more !

What if the actual function is                   k(x)  =  512ˣ
that is,  512 raised to the 'x' power ?
That would be a horse of a different cruller.

Let's try THAT out.

First, here are two facts that we'll need:

         ==>  512 ^ 1/3  =  8
and
         ==>  512 ^ 1/9  =  2 .

OK. NOW ...

Try 'A':  k(2/3) = (512) ^ 2/3  =  8^2 = 64             yes !

Try 'B':  k(4/9)  =  (512) ^ 4/9  =  2^4  =  16        yes !

Try 'C':  k(1/3)  =  (512) ^ 1/3  =  8                      yes !

Try 'D':  k(2/9)  =  (512) ^ 2/9  =  2^2  =  4  not  8 .

So here's what we have learned:

-- The function in the question is actually    k(x) = 512 ^ x

-- Choice-D is the incorrect one.