$\displaystyle 3^4*2^{-8} = \frac{3^4}{2^8}$
why not
$\displaystyle \frac{3^4}{\frac{1}{2^8}}$
as $\displaystyle \frac{1}{2^8}$ is the reciprocal of $\displaystyle \frac{2^{-8}}{1}$
So multiplying by a given number gives the same result as multiplying it by it's reciprocal!??
I thought the idea was to invert the operation? Meaning dividing by a given number is the same as multiplying by it's reciprocal and dividing by a given number is the same as multiplying by it's reciprocal?
If that's the case, how come the operation on the number here isn't inverted when we subsitutue it for it's reciprocal?