Derivatives, brief mathematical identity question

CFA Level I
#1

Hi guys I have a very simple question about a mathematical identity that I’am confused about

Is:
Fo(T) * (1+rf)^-(T-t)

The same as:
Fo(T) / (1+rf)^(T-t)

#2

Yes.

2^(-1) is the same as 1/2

#3

Yes.

More generally:

a^{-b} = \frac{1}{a^b}
#4

Thanks for that. Also do you know why we do (T-t) in the case of pricing forwards or futures instead of (t/T) as we do for most other calculations?

#5

My pleasure.

Because the units on r are \dfrac{\%}{year}, so you have to multiply it by something whose units are years to get a percentage. \dfrac tT would be unitless: just a number.

What sorts of other calculations do you mean?