You need a Windows 8 Professional Product Key to install a legitimate version, let alone Activate it!
Unless you mean 'can you upgrade Windows 7 Home Basic or Home Premium to Windows 8', then the answer is 'yes'. You can check by running the Upgrade Assistant. http://view.atdmt.com/action/FY13_Win8_Buy_DownloadPro_...
You may not use the key of windows 7 home basic to activate windows 8 pro in your own computer, because they are two different versions of windows OS. If you want to activate windows 8 pro, you need to buy a new product key. Of course, you can buy the product key from the microsoft official shop, but it's so expensive.
so i suggest you buy it from some online MSDN partner shop, like Go2keys, with cheap price.
my windows 8 product key was bought there. genuine key with fast shipping, now my win8 OS has been activated one year. feel good! hope it can help you!