will acrobat 9 pro extended work with windows 7

If Acrobat 9 is updated it will work with Windows 7. Specific programs for Windows 7 might not work, for example, MS Office 2010. So in the long run as you add newer programs or upgrade programs, you will eventually need to upgrade to Acrobat X or a newer version of Acrobat.

To add to George's answer.
If you use Office 2010 applications and expect to use Acrobat's PDFMaker you will have to use Acrobat X.

A good reference:
http://helpx.adobe.com/acrobat/kb/compatible-web-browsers-pdfmaker-applications
.html

Be well...