You can find powers for both 256 and 6561 by sketching out their prime factorization trees (I've attached a few pictures of those trees), and doing so gets us the results of:
[tex]256=2^8\\
6561=3^8[/tex]
Which makes our fraction
[tex] \frac{2^8}{3^8} [/tex]
or simply
[tex] \big(\frac{2}{3}\big)^8 [/tex]
