What camera is that with this Exif format?
I recognize the math, but not the values.
The regular math is this way:
If you simply number the f/stops starting at
f/1 = stop number 0,
f/1.4 = stop number 1,
f/2 = stop number 2,
f/2.8 = stop number 3, etc...
then f/stop = sqrt(2^stop number).
Regular math is that sqrt(2^a power) is just sqrt(2)^a power. If you move the 2 outside the radical, it must become square root out there.
The actual f/stop numbers are themselves actually powers of sqrt(2)
(f/1, f/1.414, f/2, f/2.828, f/4, etc),
so then the same math is just:
f/2.8 = stop number 3, so
f/2.8 = 1.414^3 = 2.828 precise.
or your sqrt(2^3) is the same value.
Fractions work too, and f/1.8 is 1/3 stop less than f/2, which is stop number (2 - 1/3) = 1.6667,
so f/1.8 is 1.414^1.6667 = f/1.78, which is the exact precise value (that is an exact third stop under the exact value f/2). The f/1.8 is just its nominal value, rounded so to speak, just to show humans. But the precise value is f/1.78.
Shutter speeds work the same way but their stop values are 1,2,4,8,16,32, etc seconds, (those numbers which are powers of 2 not needing the extra sqrt)
2^3 = 8 seconds.
2^-3 = 1/8 second.
So your ShutterSpeedValue of (8643856, 1000000)
would be 2^8.643856 = 400 seconds.
The shutter sequence 1,2,4,8,16,32,64,128,256,512
shows that stop number 8.6+ would be a big number.
If this value may be assumed negative, then
2^-8.643856 = 1/400 second
But then any speeds longer than 1 second would be a problem (or maybe there is some external flag?) And these are nominals too, not the precise values. Which seems very strange to me.
From your fraction (1695994/1000000),
your math.sqrt(math.pow(2, 1.695994))
intends it to be a "stop number". But it computes f/1.800, but which is a nominal number (existing in name only, not a real value), and the actual standard precise value (that works with EV powers of 2) should be f/1.78.
More about this standard math method at my site
So I'm curious where these (1695994/1000000) numbers came from?
The technique of scaling it up, with x 1000 or x 1000000 is normal, known and seen, and then the CPU chip does not need floating point math capability then. But I question it computing a nominal number? Maybe the firmware maybe could try to compensate it to be shown to a user as f/1.8, but f/1.8 or 1/400 second are not the precise numbers for the camera to use to compute EV and exposure.