Some textbooks say that atmosphere extends up to 1600 km, but exosphere is more than 9000 km thick.
Where is the mistake?
I agree with the comments; some upfront research would be good here, even at a basic level. A good place to start is this Wikipedia article, which gives not only atmospheric heights but also other characteristics such as composition and the behavior of molecules.
In terms of heights the Wikipedia article suggests 700 km for the lower boundary of the exosphere, versus 1600 km in the question. Neither figure is really wrong because, of course, when you're dealing with atmospheres there is no hard and fast boundary between layers. Similarly, the 10,000 km altitude given for the top of the exosphere, where it merges with the solar wind, is not hard and fast either; it depends on how you decide where the solar wind becomes dominant over the molecules bound by Earth's gravity.
Moreover, the outer boundary of the exosphere, however you define it, should not really be considered spherical. The solar wind moves outwards from the Sun, so the exosphere is compressed on the side facing the Sun and pulled out like the tail of a comet on the opposite side. The same effect is seen with our (and other planets') magnetosphere, because the solar wind also contains electrically charged particles.
I hope I've whetted your appetite for more in-depth exploration. Good luck!