6 is trivially 2(3) and seeing that all bases except 108 are 2 and 3 (which are prime numbers), I would immediately think of factoring 108. 108 is even so obviously 108= 2(54). Then 54= 2(27) so 108= 2^2(27). But 27 is 3^3 so 108= (2^2)(3^3). Now write every thing in powers of 2 and 3 (there are NO irrational exponents in this problem and the only rational exponents are integers).
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