Powershell and path environment variable - powershell

Question

I would like powershell to use the environment variable "PATH" to resolve executables. I'm sure it should be able to do this, but here is what I get.
PS C:\> $PSVersionTable.PSVersion
Major Minor Build Revision
----- ----- ----- --------
4 0 -1 -1
PS C:\> ${ENV:PATH} = "C:\WINDOWS\System32\"
PS C:\> ls ${ENV:PATH}\cmd.exe
Directory: C:\WINDOWS\System32
Mode LastWriteTime Length Name
---- ------------- ------ ----
-a--- 22/08/2013 8:03 PM 355840 cmd.exe
PS C:\> & cmd.exe
& : The term 'cmd.exe' is not recognized as the name of a cmdlet, function, script file, or operable program. Check
the spelling of the name, or if a path was included, verify that the path is correct and try again.
At line:1 char:3
+ & cmd.exe
+ ~~~~~~~
+ CategoryInfo : ObjectNotFound: (cmd.exe:String) [], CommandNotFoundException
+ FullyQualifiedErrorId : CommandNotFoundException

Answer 1

Run Get-Command -Type Application to see what PowerShell is seeing as valid executables.
You may find a clue as to what's going on, such as all of the listed applications have (or don't have) a certain extension, which could indicate a problem with the PATHEXT environment variable.