8^? = 256?

Since both 8 and 256 are multiples of 2, by playing with exponents on 2, I got:

          2^3 = 8     and     2^8 = 256

So now,    8^?  =  256     becomes     (2³)^?  =  2^8

When you are raising an exponent to an exponent, multiply the exponents together, so now we have:

         2^(3·?)  =  2^8

This becomes:  3·?  =  8        --->   ?  =  8/3

$${{\mathtt{8}}}^{{\mathtt{2.666\: \!666\: \!666\: \!666\: \!666\: \!7}}} = {\mathtt{256}}$$