The negative one power isn't being applied to the frames, we're dealing with frames * inverse seconds

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also, fp^-1 makes no sense, fps is shorthand for frames per second, "per" is not a unit unto itself, it's telling us that seconds are inverse (1/s, or s^-1). At no point are we dealing with inverse frames. just like Miles per hour tells us that if you're going 80mph, you are travelling at 80 miles per every 1 hour, 80m/h. So it's modifying the unit that comes after, not before. Per is just a verbal way to say "/", you could say "over", or any other equivalent statement as well.

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Frames per second = number of frames in a second

this is represented as (X Frames / second)

This can also be represented as:
>Frame Hertz

>>fHz

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since Hz is itself shorthand for inverse seconds (1/s, s^-1)

>X Frames * Hz

>>= XFrames *1/s

>>> =X frames/s

>>>>= frames * s^-1

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Now, if we have inverse Hz (Hz^-1) (since that's what I was addressing)

then it's 1/(1/s)
OR

1/(s^-1)

therefore

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X Frames * Hz^-1

> =XFrames *(1/Hz)

>> =X Frames * (1/(1/s))

>>> = Xframes * s

>>>> fs