Probably a simple answer to this...

Could somebody here please inform me how 2/(2^(8) is the same as 1/(2^(7)?

I can't seem to figure out any logical answer explaining how halving the numerator changers the exponent on the denominator by -1?

I'm sure i'm being an idiot here but I can't figure it out.

2/2^8 = 2/2x2x2x2x2x2x2x2

The 2 in the numerator cancels one of the 2's in the denominator hence:

1/2^7 = 1/2x2x2x2x2x2x2

Ah, so I was being an idiot. Thanks! that's cleared it up.