Rewrite the expressions in each pair so that they have the same base. c) (1 / 2) ^2x and (1 / 4) ^x - 1

I'm not completely sure but this is what I would do.

evaluate (1 / 4) ^x - 1 as is. But change the (1 / 2) ^2x to (2/4) ^2x. This way both fractions have the same denominator and in this sense, the same base. The 2/4 base still evaluates into 1/2 so nothing, mathematically, is being broken here.