I have two directories in my root: /dev and /live.
/dev
/live
All content inside these directories have relative paths such as /css/style.css
/css/style.css
RewriteBase lets you fix issues with how URLs get translated to file paths and back again. It's not for what you're using it for. Use a standard RewriteRule
RewriteRule
RewriteCond %{REQUEST_URI} !^/live RewriteRule ^(/?)(.*) /live/$2