重写导致404

Question

I am trying to do a simple URL rewrite and I have searched apache.org and SO for an answer but have come up short. I executed the request and watched with a network utility and the server is throwing a 404. I am really sorry to be posting this simple question but I really don't see why this rule is not working. Thanks

I want to have this SEO-friendly url format

/products/my-product

Go to this physical file in the file system

/my-product.php

BTW: The folder "products" does not exist; it's just there for SEO reasons

Here is my .htaccess (Removing "RewriteBase /") has no effect

RewriteEngine   on
RewriteBase /
Options +FollowSymLinks


RewriteRule ^products/([A-Za-z\-]+)/?$ $1.php [L,QSA,NC]