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After using my 80-400mm AF-S with a 1.4x TC & 1.7x TC... I don't agree with the above.
I wouldn't recommend the 1.7x. However, the 1.4x TC performed very well if you can afford to lose the stop of light. Obviously, f/8 isn't a great place to start if you're shooting in low light but the autofocus is still very good on the D7100 and the image quality, though not quite as sharp as the bare lens, is still excellent.
Obviously, everything is situational. If the extra stop of light is going to let you capture a sharp image, well, cropping a sharp image is better than not cropping a blurry or excessively noisy image. But for this combo, cropping a shot out of the 80-400mm AF-S is not as good as a shot with the 1.4x attached. I didn't directly try it, but my impression is that cropping as shot with the 1.4x TC is similar to a shot with the 1.7x TC - I didn't like the softening I was seeing with the 1.7x.
My only caveats being that I noticed my 80-400mm AF-S + TC-14E II required a massive autofocus fine-tune, to the order of something like +16. When I first started shooting with it, I was getting terrible shots because the AF was so far off. Also, that focal length is distinctly into the "tricky to hand-hold" range.
All that said - I don't use the 1.4x much. I'd rather shoot without it, and the time it takes to put it on is not very conducive to a quick, that-animal-is-a-little-too-far-away situation. However, if you're going to be doing something where you know 400mm is too short, it works pretty well.