For example, if you own 10,000 shares of a company and it declares a one for ten reverse split, you will own a total of 1,000 shares after the split.
If you paid $5,000 (for example) for those 10,000 shares, you had a cost basis of $5000 or 50 cents a share. For the 1000 shares you now have, you still have a cost basis of $5000, but it's now $5 per share.
